[1] Abramowitz, M., Stegun, I. (1964) Handbook of Mathematical Functions, Dover.
[2] Adler, R.J. (1981) The Geometry of Random Fields, J. Wiley.
[3] Adler, R.J., Taylor, J.E. (2007) Random Fields and Geometry, Springer-Verlag.
[4] Anderes, E., Chatterjee, S. (2009) Consistent estimates of deformed isotropic Gaussian random fields on the plane, Annals of Statistics, 37, No. 5A, 2324–2350.
[5] Antoine, J.-P., Vandergheynst, P. (1999) Wavelets on the sphere: a group-theoretic approach, Applied and Computational Harmonic Analysis, 7, 262–291.
[6] Antoine, J.-P., Vandergheynst, P. (2007) Wavelets on the sphere and other conic sections, Journal of Fourier Analysis and its Applications, 13, 369–386.
[7] Arjunwadkar, M., Genovese, C.R., Miller, C.J., Nichol, R.C., Wasserman, L. (2004) Nonparametric inference for the Cosmic Microwave Background, Statistical Science, 19, 308–321.
[8] Babich, D., Creminelli, P., Zaldarriaga, M. (2004) The shape of non-Gaussianities, Journal of Cosmology and Astroparticle Physics, 8, 009.
[9] Balbi, A. (2007), The Music of the Big Bang, Springer-Verlag.
[10] Baldi, P., Marinucci, D. (2007). Some characterizations of the spherical harmonics coefficients for isotropic random fields, Statistics & Probability Letters, 77(5), 490–496.
[11] Baldi, P., Marinucci, D., Varadarajan, V.S. (2007) On the characterization of isotropic random fields on homogeneous spaces of compact groups, Electronic Communications in Probability, 12, 291–302.
[12] Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D. (2008) High frequency asymptotics for wavelet-based tests for Gaussianity and isotropy on the torus, Journal of Multivariate Analysis, 99(4), 606–636.
[13] Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D. (2009) Asymptotics for Spherical Needlets, Annals of Statistics, 37(3), 1150–1171, arxiv:math/0606599.
[14] Baldi, P., Kerkyacharian, G.Marinucci, D., Picard, D. (2009) Subsampling Needlet Coefficients on the Sphere, Bernoulli, 15(2), 438–463, arxiv 0706.4169.
[15] Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D. (2009) Density estimation for directional data using needlets, Annals of Statistics, 37(6A), 3362–3395.
[16] Baldi, P., Kerkyacharian, G., Marinucci, D., Picard, D. (2009) Besov spaces for sections of spin fiber bundles on the sphere, preprint.
[17] Balkar, E., Lovesey, S.W. (2009), Introduction to the Graphical Theory of Angular Momentum, Springer Tracts on Modern Physics, Springer.
[18] Bartolo, N., Komatsu, E., Matarrese, S., Riotto, A. (2004). Non-Gaussianity from inflation: theory and observations, Physical Reports, 402, 103–266.
[19] Bartolo, N., Matarrese, S., Riotto, A. (2010) Non-Gaussianity and the Cosmic Microwave Background anisotropies, Advances in Astronomy, in press, arXiv: 1001.3957.
[20] Bartolo, N., Fasiello, M., Matarrese, S., Riotto, A. (2010) Large non-Gaussianities in the effective field theory approach to single-field inflation: the bispectrum, Journal of Cosmology and Astroparticle Physics, 1008:08, arXiv: 1004.0893.
[21] Bennett, C. L., Halpern, M., Hinshaw, G., Jarosik, N., Kogut, A., Limon, M., Meyer, S. S., Page, L., Spergel, D. N., Tucker, G. S., Wollack, E., Wright, E. L., Barnes, C., Greason, M. R., Hill, R. S., Komatsu, E., Nolta, M. R., Odegard, N., Peiris, H. V., Verde, L., Weiland, J. L. (2003) First -Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: preliminary maps and basic results, Astrophysical Journal Supplement Series, Volume 148, Issue 1, pp. 1–27.
[22] Bennett, C. L., Hill, S., Hinshaw, G., Larson, D., Smith, K. M., Dunkley, J., Gold, B., Halpern, M., Jarosik, N., Kogut, A., Komatsu, E., Limon, M., Meyer, S. S., Nolta, M. R., Odegard, N., Page, L., Spergel, D. N., Tucker, G. S., Weiland, J. L., Wollack, E., Wright, E. L. (2010) Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: are there Cosmic Microwave Background anomalies?, arXiv: 1001.4758.
[23] Biedenharn, L.C., Louck, J.D. (1981) The Racah-Wigner Algebra in Quantum Theory, Encyclopedia of Mathematics and its Applications, Volume 9, Addison-Wesley.
[24] Billingsley, P. (1968) Convergence of Probability Measures, J. Wiley.
[25] Bishop, R.L., Goldberg, S. (1980) Tensor Analysis on Manifolds, Dover.
[26] Blei, R. (2001) Analysis in Integer and Fractional Dimensions, Cambridge University Press.
[27] Breuer, P., Major, P. (1983) Central limit theorems for nonlinear functionals of Gaussian fields, Journal of Multivariate Analysis, 13, no. 3, 425–441.
[28] Bridles, S. et al. (2009) Handbook for the GREAT08 Challenge: An image analysis competition for cosmological lensing, Annals of Applied Statistics, Vol. 3, No. 1, 6–37.
[29] Brillinger, D. W. (1975) Time series. Data Analysis and Theory, Holt, Rinehart and Winston.
[30] Brockwell, P.J., Davis, R.A. (1991) Time Series: Theory and Methods, Second edition, Springer Series in Statistics, Springer-Verlag.
[31] Brocker, T., tom Dieck, T. (1985) Representations of Compact Lie Groups, Graduate Texts in Mathematics, 98, Springer-Verlag.
[32] Bump, D. (2005) Lie Groups, Graduate Texts in Mathematics, 225, Springer-Verlag.
[33] Cabella, P., Kamionkowskii, M. (2005) Theory of Cosmic Microwave Background Polarization, Lectures given at the 2003 Villa Mondragone School of Gravitation and Cosmology: “The Polarization of the Cosmic Microwave Background,” Rome, arxiv: astro.ph/0403392.
[34] Cabella, P., Hansen, F.K., Marinucci, D., Pagano, D., Vittorio, N. (2004) Search for non-Gaussianity in pixel, harmonic, and wavelet space: compared and combined, Physical Review D, 69, 063007.
[35] Cabella, P., Hansen, F.K., Liguori, M., Marinucci, D., Matarrese, S., Moscardini, L., Vittorio, N. (2005) Primordial non-Gaussianity: local curvature method and statistical significance of constraints on fNL from WMAP data, Monthly Notices of the Royal Astronomical Society, Vol. 358, pp. 684–692.
[36] Cabella, P., Hansen, F.K., Liguori, M., Marinucci, D., Matarrese, S., Moscardini, L., Vittorio, N. (2006) The integrated bispectrum as a test of CMB non-Gaussianity: detection power and limits on fNL with WMAP data, Monthly Notices of the Royal Astronomical Society, 369, 819–824, arxiv: astro-ph/0512112.
[37] Cabella, P., Marinucci, D. (2009) Statistical challenges in the analysis of Cosmic Microwave Background radiation, Annals of Applied Statistics, 3(1), 61–95.
[38] Chambers, D., Slud, E. (1989) Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems, Stochastic Processes and their Applications, 32(1), 93–107.
[39] Chambers, D., Slud, E. (1989) Central Limit Theorems for nonlinear functionals of stationary Gaussian processes, Probability Theory and Related Fields, 80(3), 323–346.
[40] Cruz, M., Cayon, L., Martinez-Gonzalez, E., Vielva, P., Jin, J., (2007) The non-Gaussian Cold Spot in the 3-year WMAP Data, Astrophysical Journal, 655, 11–20.
[41] Cruz, M., Cayon, L., Martinez-Gonzalez, E., Vielva, P., (2006) The non-Gaussian Cold Spot in WMAP: significance, morphology and foreground contribution, Monthly Notices of the Royal Astronomical Society, 369, 57–67.
[42] Dahlke, S., Steidtl, G., Teschke, G. (2007) Frames and coorbit theory on homogeneous spaces with a special guidance on the sphere, Journal of Fourier Analysis and its Applications, 13, 387–404.
[43] Davidson, J. (1994), Stochastic Limit Theory, Oxford University Press.
[44] De Bernardis, P. et al. (2000) A flat Universe from high-resolution maps of the Cosmic Microwave Background radiation, Nature, Vol. 404, Issue 6781, pp. 955–959.
[45] de Gasperis, G., Balbi, A., Cabella, P., Natoli, P., Vittorio, N. (2005) ROMA: A map-making algorithm for polarised CMB data sets, Astronomy and Astrophysics, Vol. 436, Issue 3, pp. 1159–1165.
[46] Delabrouille, J., Cardoso, J.-F., Le Jeune, M., Betoule, M., Fay, G., Guilloux, F. (2009) A full sky, low foreground, high resolution CMB map from WMAP, Astronomy and Astrophysics, Vol. 493, Issue 3, pp. 835–857, arXiv:0807.0773.
[47] Dennis, M. (2004), Canonical representation of spherical functions: Sylvester's theorem, Maxwell's multipoles and Majorana's sphere, Journal of Physics A, 37, 9487–9500.
[48] Dennis, M. (2005) Correlations between Maxwell's multipoles for Gaussian random functions on the sphere, Journal of Physics A, 38, 1653–1658.
[49] Diaconis, P. (1988) Group Representations in Probability and Statistics, IMS Lecture Notes – Monograph Series, 11, Hayward.
[50] Diaconis, P., Freedman, D. (1987) A dozen de Finetti-style results in search of a theory, Annales Institute Henri Poincaré Probabilités et Statistiques, 23(2), 397–423.
[51] Dodelson, S. (2003) Modern Cosmology, Academic Press.
[52] Doré, O., Colombi, S., Bouchet, F.R. (2003) Probing non-Gaussianity using local curvature, Monthly Notices of the Royal Astronomical Society, 344, 905–916.
[53] Doroshkevich, A.G., Naselsky, P.D., Verkhodanov, O.V., Novikov, D.I., Turchaninov, V.I., Novikov, I.D., Christensen, P.R., Chiang, L.-Y. (2005) Gauss-Legendre Sky Pixelization (GLESP) for CMB Maps, International Journal of Modern Physics D, 14, 275.
[54] Doukhan, P. (1988) Formes de Toeplitz associées à une analyse multi-échelle, (French) [Toeplitz forms associated to a multiscale analysis]Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 306, no. 15, 663–666.
[55] Doukhan, P., Leon, J. R. (1990) Formes quadratique d'estimateurs de densité par projections orthogonales. (French) [Quadratic deviation of projection density estimates]Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 310, no. 6, 425–430.
[56] Dudley, R.M. (2002) Real Analysis and Probability, revised reprint of the 1989 original, Cambridge Studies in Advanced Mathematics, 74, Cambridge University Press.
[57] Duistermaat, J.J., Kolk, J.A.C. (1997) Lie Groups, Springer-Verlag.
[58] Duffin, R.J., Schaeffer, A.C. (1952) A class of nonharmonic Fourier series, Transactions of the American Mathematical Society, 72, 341–366.
[59] Durastanti, C., Geller, D., Marinucci, D. (2010) Nonparametric Regression on Spin fiber Bundles, under revision for the Journal of Multivariate Analysis, arXiv preprint 1009.4345.
[60] Durrer, R. (2008) The Cosmic Microwave Background, Cambridge University Press.
[61] Efstathiou, G. (2004) Myths and truths concerning estimation of power spectra: the case for a hybrid estimator, Monthly Notices of the Royal Astronomical Society, 349, Issue 2, pp. 603–626.
[62] Eriksen, H.K., Hansen, F.K., Banday, A.J., Gorski, K.M., Lilje, P.B. (2004) Asymmetries in the CMB anisotropy field, Astrophysical Journal, 605, 14–20.
[63] Faraut, J. (2006) Analyse sur le Groupes de Lie, Calvage et Mounet.
[64] Faÿ, G., Guilloux, F., Betoule, M., Cardoso, J.-F., Delabrouille, J., Le Jeune, M. (2008) CMB power spectrum estimation using waveletsPhysical Review D, 78:083013.
[65] Faÿ, G., Guilloux, F. (2008) Consistency of a Needlet Spectral Estimator on the Sphere, arXiv:0807.2162.
[66] Feller, W. (1970) An Introduction to Probability Theory and its Applications, Volume II, 2nd Edition J. Wiley.
[67] Fergusson, J.R., Liguori, M., Shellard, E.P.S. (2009) General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of fNL, arXiv: 0912.5516.
[68] Fergusson, J.R., Liguori, M., Shellard, E.P.S. (2010) The CMB Bispectrum, arXiv: 1006.1642.
[69] Foulds, L.R. (1992) Graph Theory and Applications, Universitext, Springer-Verlag.
[70] Freeden, W., Schreiner, M. (1998) Orthogonal and nonorthogonal multiresolution analysis, scale discrete and exact fully discrete wavelet transform on the sphere. Constructive Approximations, 14, 4, 493–515.
[71] Gangolli, R. (1967) Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy's Brownian motion of several parameters. Annales de l'Institut H. Poincaré Sect. B, Vol. 3, 121–226.
[72] Geller, D., Hansen, F.K., Marinucci, D., Kerkyacharian, G., Picard, D. (2008), Spin needlets for Cosmic Microwave Background Polarization data analysis, Physical Review D, D78:123533, arXiv:0811.2881.
[73] Geller, D., Lan, X., Marinucci, D. (2009) Spin needlets spectral estimation, Electronic Journal of Statistics, Vol. 3, 1497–1530, arXiv:0907.3369.
[74] Geller, D., Marinucci, D. (2008) Spin wavelets on the sphere, Journal of Fourier Analysis and its Applications, Vol. 16, Issue 6, pages 840–884, arXiv: 0811.2835.
[75] Geller, D., Marinucci, D. (2011) Mixed needlets, Journal of Mathematical Analysis and Applications, Vol. 375, n.2, pp. 610–630, arXiv: 1006.3835.
[76] Geller, D., Mayeli, A. (2009) Continuous wavelets on manifolds, Mathematische Zeitschrift, Vol. 262, pp. 895–927, arXiv: math/0602201.
[77] Geller, D., Mayeli, A. (2009) Nearly Tight frames and space-frequency analysis on compact manifolds, Mathematische Zeitschrift, Vol. 263 (2009), pp. 235–264, arXiv: 0706.3642.
[78] Geller, D., Mayeli, A. (2009) Besov spaces and frames on compact manifolds, Indiana University Mathematics Journal, Vol. 58, pp. 2003–2042, arXiv:0709.2452.
[79] Geller, D., Mayeli, A. (2009) Nearly tight frames of spin wavelets on the sphere, Sampling Theory in Signal and Image Processing, in press, arXiv:0907.3164.
[80] Geller, D., Pesenson, I. (2010), Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds, Journal of Geometric Analysis, in press, arXiv:1002.3841.
[81] Genovese, C.R., Perone-Pacifico, M., Verdinelli, I., Wasserman, L. (2009) On the path density of a gradient field. Annals of Statistics, 37(6A), 3236–3271.
[82] Genovese, C.R., Perone-Pacifico, M., Verdinelli, I., Wasserman, L. (2010) Non-parametric filament estimation, arXiv:1003.5536.
[83] Ghosh, T., Delabrouille, J., Remazeilles, M., Cardoso, J.-F., Souradeep, T. (2010) Foreground maps in WMAP frequency bands, arxiv: 1006.0916.
[84] Goldberg, J.N., Newman, E.T., (1967) Spin-s Spherical Harmonics and ð, Journal of Mathematical Physics, 8(11), 2155–2166.
[85] Gorski, K.M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., Bartelman, M., (2005) HEALPix – A framework for high resolution discretization, and fast analysis of data distributed on the sphere, Astrophysical Journal, 622, 759–771.
[86] Gradshteyn, I. S., Ryzhik, I. M. (1980) Table of Integrals, Series, and Products, Academic Press.
[87] Guilloux, F., Fay, G., Cardoso, J.-F. (2008) Practical wavelet design on the sphere, Applied and Computational Harmonic Analysis, 26, no. 2, 143–160.
[88] Guionnet, A. (2009) Large random matrices: lectures on macroscopic asymptotics. Lecture Notes in Mathematics, Vol. 1957, Springer-Verlag.
[89] Guivarc'h, Y., Keane, M. and Roynette, B. (1977) Marches Aléatoires sul les Groupes de Lie, Lecture Notes in Mathematics, Vol. 624, Springer-Verlag.
[90] Hamann, Jan, Wong, Yvonne, Y. Y. (2008) The effects of Cosmic Microwave Background (CMB) temperature uncertainties on cosmological parameter estimation, Journal of Cosmology and Astroparticle Physics, Issue 03, pp. 025.
[91] Hanany, S., Ade, P., Balbi, A., Bock, J., Borrill, J., Boscaleri, A., de Bernardis, P., Ferreira, P. G., Hristov, V. V., Jaffe, A. H., Lange, A. E., Lee, A. T., Mauskopf, P. D., Netterfield, C. B., Oh, S., Pascale, E., Rabii, B., Richards, P. L., Smoot, G. F., Stompor, R., Winant, C. D., Wu, J. H. P. (2000) MAXIMA-1: A measurement of the Cosmic Microwave Background anisotropy on angular scales of 10'-5°, The Astrophysical Journal, Vol. 545, Issue 1, L5–L9.
[92] Hannan, E.J. (1970) Multiple Time Series. J. Wiley.
[93] Hansen, F.K., Cabella, P., Marinucci, D., Vittorio, N. (2004) Asymmetries in the local curvature of the WMAP data, Astrophysical Journal Letters, L67–L70.
[94] Hardle, W., Kerkyacharian, G., Picard, D. and Tsybakov, A. (1998) Wavelets, Approximation, and Statistical Applications, Springer Lecture Notes in Statistics, 129.
[95] Hausman, J.A. (1978) Specification tests in econometrics, Econometrica, 6, 1251–1271.
[96] Havin, V. and Joricke, B. (1994) The Uncertainty Principle in Harmonic Analysis, Springer-Verlag.
[97] Hernandez, E., Weiss, G. (1996) A First Course on Wavelets, Studies in Advanced Mathematics, CRC Press.
[98] Hikage, C., Matsubara, T., Coles, P., Liguori, M., Hansen, F.K., Matarrese, S. (2008) Primordial non-Gaussianity from Minkowski functionals of the WMAP temperature anisotropies, Monthly Notices Royal Astronomical Society, 389:1439–1446.
[99] Hinshaw, G., Weiland, J. L., Hill, R. S., Odegard, N., Larson, D., Bennett, C. L., Dunkley, J., Gold, B., Greason, M. R., Jarosik, N., Komatsu, E., Nolta, M. R., Page, L., Spergel, D. N., Wollack, E., Halpern, M., Kogut, A., Limon, M., Meyer, S. S., Tucker, G. S., Wright, E. L. (2009) Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: data processing, sky maps, and basic results, Astrophysical Journal Supplement Series, 180:225–245.
[100] Hivon, E., Gorski, K.M., Netterfield, C.B., Crill, B.P., Prunet, S., Hansen, F.K. (2002) MASTER of the Cosmic Microwave Background anisotropy power spectrum: a fast method for statistical analysis of large and complex Cosmic Microwave Background data sets, Astrophysical Journal, Volume 567, Issue 1, pp. 2–17.
[101] Holschneider, M., Iglewska-Nowak., I. (2007) Poisson wavelets on the sphereJournal of Fourier Analysis and its Applications, 13, 405–420.
[102] Hu, W. (2001) The angular trispectrum of the Cosmic Microwave Background, Physical Review D, Volume 64, Issue 8, id.083005.
[103] Hu, Y., Nualart, D. (2005) Renormalized self-intersection local time for fractional Brownian motion, The Annals of Probability, 33(3), 948–983.
[104] Ivanov, A.V., Leonenko, N.N. (1989), Statistical Analysis of Random Fields, Kluwer.
[105] Jansson, S. (1997) Gaussian Hilbert Spaces, Cambridge University Press.
[106] Johnson, N.L., Kotz, S.J. (1972) Distributions in Statistics: Continuous Multivariate Distributions, J. Wiley.
[107] Kagan, A.M., Linnik, Y.V., Rao, C.R. (1973) Characterization Problems in Mathematical Statistics, J. Wiley.
[108] Kamionkowski, M., Kosowski, A., Stebbins, A. (1997) Statistics of Cosmic Microwave Background Polarization, Physical Review D, 55, 7368–7388.
[109] Keihänen, E., Kurki-Suonio, H., Poutanen, T. (2005) MADAM- a map-making method for CMB experiments, Monthly Notices of the Royal Astronomical Society, Vol. 360, Issue 1, pp. 390–400.
[110] Kerkyacharian, G., Petrushev, P., Picard, D., Willer, T. (2007) Needlet algorithms for estimation in inverse problems, Electronic Journal of Statistics, 1, 30–76.
[111] Kerkyacharian, G., Nickl, R., Picard, D. (2010) Concentration inequalities and confidence bands for needlet density estimators on compact homogeneous manifolds, Probability Theory and Related Fields, in press, arXiv:1102.2450.
[112] Kerkyacharian, G., Pham Ngoc, T.M., Picard, D. (2009) Localized spherical deconvolution, Annals of Statistics, in press, arXiv: 0908.1952.
[113] Kim, P.T., Koo, J.-Y. (2002) Optimal spherical deconvolution, Journal of Multivariate Analysis, 80, 21–42.
[114] Kim, P.T., Koo, J.-Y., Luo, Z.-M. (2009) Weyl eigenvalue asymptotics and sharp adaptation on vector bundles, Journal of Multivariate Analysis, 100, 1962–1978.
[115] Kitching, T. et al. (2010) Gravitational lensing accuracy testing 2010 (GREAT10) challenge handbook, preprint, arXiv: 1009.0779.
[116] Kolb, E., Turner, M. (1994), The Early Universe, Cambridge University Press.
[117] Komatsu, E., Spergel, D.N. (2001) Acoustic signatures in the primary Microwave Background bispectrum, Physycal Review D, 63, 063002.
[118] Komatsu, E.Wandelt, B.D., Spergel, D.N., Banday, A.J., Gorski, K.M. (2002), Measurement of the Cosmic Microwave Backgroun bispectrum on the COBE DMR sky maps, Astrophysical Journal, 566, 19–29.
[119] Komatsu, E., Yadav, A., Wandelt, B. (2007) Fast estimator of primordial non-Gaussianity from temperature and polarization anisotropies in the Cosmic Microwave Background, Astrophysical Journal, 664:680–686.
[120] Komatsu, E., Yadav, A., Wandelt, B., Liguori, M., Hansen, F.K., Matarrese, S. (2008) Fast estimator of primordial non-Gaussianity from temperature and polarization anisotropies in the Cosmic Microwave Background II: partial sky coverage and inhomogeneous noise, Astrophysical Journal 678:578.
[121] Komatsu, et al. (2009) Five-Year Wilkinson Microwave Anisotropy Probe observations: cosmological interpretation, Astrophysical Journal Supplement Series, 180, 2, 330–376.
[122] Koornwinder, T.H. (2008), Representations of SU(2) and Jacobi polynomials, preprint, available online http://staff.science.uva.nl/ thk/edu/orthopoly.pdf.
[123] Lan, X., Marinucci, D. (2008) The needlets bispectrum, Electronic Journal of Statistics, 2, 332–367.
[124] Lan, X., Marinucci, D. (2009) On the dependence structure of wavelet coefficients for spherical random fields, Stochastic Processes and their Applications, 119, 3749–3766.
[125] Leonenko, N. (1999) Limit Theorems for Random Fields with Singular Spectrum, Kluwer.
[126] Leonenko, N., Sakhno, L. (2009) On spectral representations of tensor random fields on the sphere, arXiv:0912.3389.
[127] Liboff, R.L. (1999) Introductory Quantum Mechanics, Addison-Wesley.
[128] Magnus, J.R., Neudecker, H. (1988) Matrix Differential Calculus with Applications to Statistics and Econometrics, J. Wiley.
[129] Malyarenko, A. (2009) Invariant random fields in vector bundles and application to cosmology, preprint arXiv: 0907.4620.
[130] Marinucci, D. (2004) Testing for non-Gaussianity on Cosmic Microwave Background radiation: a review, Statistical Science, 19, 294–307.
[131] Marinucci, D. (2006) High-resolution asymptotics for the angular bispectrum of spherical random fields, Annals of Statistics, 34, 1–41.
[132] Marinucci, D. (2008) A central limit theorem and higher order results for the angular bispectrum, Probability Theory and Related Fields, 141(3–4), 389–409.
[133] Marinucci, D., Piccioni, M. (2004) The empirical process on Gaussian spherical harmonics, Annals of Statistics, 32, 1261–1288.
[134] Marinucci, D., Peccati, G. (2008) High-frequency asymptotics for subordinated stationary fields on an Abelian compact group, Stochastic Processes and their Applications, 118 (4), 585–613.
[135] Marinucci, D., Peccati, G. (2010) Group representations and high-resolution Central Limit Theorems for subordinated spherical random fields, Bernoulli, 16, 798–824.
[136] Marinucci, D.; Peccati, G. (2010) Representations of SO(3) and angular polyspectra, Journal of Multivariate Analysis, 101, 77–100.
[137] Marinucci, D.; Peccati, G. (2010) Ergodicity and Gaussianity for spherical random fields, Journal of Mathematical Physics, 51, n. 4, 043301, 23 pp.
[138] Marinucci, D., Wigman, I. (2010) On the excursion sets of spherical Gaussian eigenfunctions, preprint, arXiv: 1009.4367.
[139] Marinucci, D., Pietrobon, D., Balbi, A., Baldi, P., Cabella, P., Kerkyacharian, G., Natoli, P., Picard, D., Vittorio, N. (2008) Spherical needlets for CMB data analysis, Monthly Notices of the Royal Astronomical Society, Vol. 383, 539–545, arXiv: 0707.0844.
[140] Mayeli, A. (2010) Asymptotic uncorrelation for Mexican needlets, Journal of Mathematical Analysis and Applications, Vol. 363, Issue 1, pp. 336–344, arXiv: 0806.3009.
[141] McEwen, J.D., Vielva, P., Wiaux, Y., Barreiro, R.B., Cayon, L., Hobson, M.P., Lasenby, A.N., Martinez-Gonzalez, E., Sanz, J. (2007) Cosmological applications of a wavelet analysis on the sphere, Journal of Fourier Analysis and its Applications, 13, 495–510.
[142] Miller, W.Topics in Harmonic Analysis with Applications to Radar and Sonar, preprint, available online http://www.ima.umn.edu/ miller/radarla.pdf.
[143] Narcowich, F.J., Petrushev, P., Ward, J.D. (2006) Localized tight frames on spheres, SIAM Journal of Mathematical Analysis, 38, 2, 574–594.
[144] Narcowich, F.J., Petrushev, P., Ward, J.D. (2006) Decomposition of Besov and Triebel-Lizorkin spaces on the sphere, Journal of Functional Analysis, 238, 2, 530–564.
[145] Natoli, P., Degasperis, G., Marinucci, D., Vittorio, N. (2002) Non-iterative methods to estimate the in-flight noise properties of CMB detectors, Astronomy and Astrophysics, 383, pp. 1100–1112.
[146] Newman, E. T., Penrose, R. (1966) Note on the Bondi-Metzner-Sachs group, Journal of Mathematical Physics, 7, 863–870.
[147] Nourdin, I., Peccati, G. and Reinert, G. (2010) Invariance principles for homogeneous sums: universality of the Gaussian Wiener chaos, Annals of Probability, 38(5), 1947–1985.
[148] Nourdin, I., Peccati, G. (2009). Stein's method on Wiener chaos, Probability Theory and Related Fields, 145(1), 75–118.
[149] Nourdin, I., Peccati, G. (2009) Stein's method meets Malliavin calculus: a short survey with new estimates. In the volume: Recent Advances in Stochastic Dynamics and Stochastic Analysis, World Scientific.
[150] Nourdin, I., Peccati, G., Réveillac, A. (2008). Multivariate normal approximation using Stein's method and Malliavin calculus, Annales de l'Institut H. Poincaré (B), 46(1), 45–58.
[151] Nualart, D. (2006) The Malliavin Calculus and Related Topics. Second edition, Springer-Verlag.
[152] Nualart, D., Peccati, G. (2005) Central limit theorems for sequences of multiple stochastic integrals, Annals of Probability, 33, 177–193.
[153] Patanchon, G., Delabrouille, J., Cardoso, J.-F., Vielva, P. (2005) CMB and foreground in WMAP first-year data, Monthly Notices of the Royal Astronomical Society, 364, pp. 1185–1194.
[154] Peacock, J.A. (1999) Cosmological Physics, Cambridge University Press.
[155] Peccati, G. (2001) On the convergence of multiple random integrals, Studia Sc. Math. Hungarica, 37, 429–470.
[156] Peccati, G. (2007) Gaussian approximations of multiple integrals, Electronic Communications in Probability 12, 350–364.
[157] Peccati, G., Pycke, J.-R. (2010) Decompositions of stochastic processes based on irreducible group representations, Theory of Probability and Applications, 54(2), 217–245.
[158] Peccati, G., Taqqu, M.S. (2008) Stable convergence of multiple Wiener-Itô integrals, Journal of Theoretical Probability, 21(3), 527–570.
[159] Peccati, G., M.S., Taqqu (2010) Wiener Chaos: Moments, Cumulants and Diagrams. A Survey with Computer Implementation, Springer-Verlag.
[160] Peccati, G., Tudor, C.A. (2005) Gaussian limits for vector-valued multiple stochastic integrals. In: Séminaire de Probabilités XXXVIII, 247–262, Springer Verlag.
[161] Peebles, J. (1993), Principles of Cosmology, Princeton University Press.
[162] Pietrobon, D., Balbi, A., Marinucci, D. (2006) Integrated Sachs-Wolfe effect from the cross correlation of WMAP 3-Year and the NRAO VLA Sky Survey Data: new results and constraints on dark energy, Physical Review D, 74, 043524.
[163] Pietrobon, D.Amblard, A., Balbi, A., Cabella, P., Cooray, A., Marinucci, D. (2008) Needlet detection of features in the WMAP CMB sky and the impact on anisotropies and hemispherical asymmetries, Physical Review D, Vol. 78, Issue 10, id. 103504.
[164] Pietrobon, D.Amblard, A., Balbi, A., Cabella, P., Cooray, A., Vittorio, N. (2009) Constraints on primordial non-Gaussianity from a needlet analysis of the WMAP-5 data, Monthly Notices of the Royal Astronomical Society, Volume 396, Issue 3, pp. 1682–1688.
[165] Pietrobon, D.Amblard, A., Balbi, A., Cabella, P., Cooray, A., Vittorio, N. (2009) Needlet bispectrum asymmetries in the WMAP 5-year Data, Monthly Notices of the Royal Astronomical Society, L367, arXiv: 0905.3702.
[166] Pietrobon, D., Balbi, A., Cabella, P.Gorski, K. M. (2010) Needatool: A Needlet Analysis Tool for Cosmological Data Processing, Astrophysical Journal, 723, 1.
[167] Polenta, G., Marinucci, D., Balbi, A., De Bernardis, P., Hivon, E., Masi, S., Natoli, P., Vittorio, N. (2005) Unbiased estimation of angular power spectra, Journal of Cosmology and Astroparticle Physics, Issue 11, n.1, pp.1–17.
[168] Pycke, J.-R. (2007) A decomposition for invariant tests of uniformity on the sphere, Proceedings of the American Mathematical Society, 135, 2983–2993.
[169] Revuz, D., Yor, M. (1999) Continuous Martingales and Brownian motion, Third edition, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293, Springer-Verlag.
[170] Robinson, P.M. (1995) Log-periodogram regression of time series with long range dependence, Annals of Statistics, 23, 1048–1072.
[171] Robinson, P.M. (1995) Gaussian semiparametric estimation of long range dependence, Annals of Statistics, 23, 1630–1661.
[172] Rosca, D. (2007) Wavelet bases on the sphere obtained by radial projection, Journal of Fourier Analysis and its Applications, 13, 421–434.
[173] Rudin, W. (1962) Fourier Analysis on Groups, Wiley Classics Library, Wiley.
[174] Rudin, W. (1975) Real and Complex Analysis, McGraw-Hill.
[175] Rudjord, O., Hansen, F.K.Lan, X., Liguori, M., Marinucci, D., Matarrese, S. (2009) An estimate of the primordial non-Gaussianity parameter fNL using the needlet bispectrum from WMAP, The Astrophysical Journal, 701:369–376, arXiv:0901.3154.
[176] Rudjord, O., Hansen, F.K.Lan, X., Liguori, M., Marinucci, D., Matarrese, S. (2010), Directional variations of the non-Gaussianity parameter fNL, Astrophysical Journal, Vol. 708, 2, 1321–1325.
[177] Schreiber, M. (1969) Fermeture en probabilité de certains sous-espaces d'un espace L2, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 14, 36–48.
[178] Schwartzman, A., Mascarenhas, W.F. and Taylor, J.E.T. (2008) Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices, Annals of Statistics, 36, no. 6, 2886–2919.
[179] Scodeller, S., Rudjord, O., Hansen, F.K., Marinucci, D., Geller, D., Mayeli, A. (2010) Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets, Astrophysical Journal, in press, arXiv: 1004.5576.
[180] Simon, B. (1996) Representations of Finite and Compact Groups, Graduate Studies in Mathematics, 10, American Mathematical Society.
[181] Seljak, U., Zaldarriaga, M. (1996) Line-of-Sight integration approach to Cosmic Microwave Background anisotropies, Astrophysical Journal, Vol.469, p.437.
[182] Senatore, L., Smith, K.M., Zaldarriaga, M. (2010) Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data, Journal of Cosmology and Astroparticle Physics, 1001:028.
[183] Serre, J.P. (1977) Linear Representation of Finite Groups, Springer-Verlag.
[184] Regan, D.M., Shellard, E.P.S. (2009), Cosmic string power spectrum, bispectrum and trispectrum, arXiv:0911.2491.
[185] Shigekawa, I. (1986) De Rham–Hodge–Kodaira's decomposition on an abstract Wiener space, Journal of Mathematics of the Kyoto University, 26, 191–202.
[186] Shyraev, A.N. (1984) Probability, Springer-Verlag.
[187] Smoot, G. F., Bennett, C. L., Kogut, A., Wright, E. L., Aymon, J., Boggess, N. W., Cheng, E. S., de Amici, G., Gulkis, S., Hauser, M. G., Hinshaw, G., Jackson, P. D., Janssen, M., Kaita, E., Kelsall, T., Keegstra, P., Lineweaver, C., Loewenstein, K., Lubin, P., Mather, J., Meyer, S. S., Moseley, S. H., Murdock, T., Rokke, L., Silverberg, R. F., Tenorio, L., Weiss, R., Wilkinson, D. T. (1992) Structure in the COBE differential microwave radiometer first-year maps, Astrophysical Journal, Part 2 - Letters, Vol. 396, no. 1, pp. L1–L5.
[188] Spergel, D.N. et al. (2003) First-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters, Astrophysical Journal Supplement Series, 148, 1, pp. 175–194.
[189] Spergel, D.N. et al. (2007) Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) observations: implications for cosmology, Astrophysical Journal Supplement Series, 170, 2, 377–408.
[190] Stein, E.M., Weiss, G. (1971) Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press.
[191] Sternberg, S.Group Theory and Physics, Cambridge University Press.
[192] Surgailis, D. (2003) CLTs for polynomials of linear sequences: Diagram formula with illustrations. In Theory and Applications of Long Range Dependence, 111–128, Birkhäuser.
[193] Szego, G. (1975) Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Volume 23 Reprinted version of the 1939 original.
[194] Varadarajan, V.S. (1999) An Introduction to Harmonic Analysis on Semisimple Lie Groups, Corrected reprint of the 1989 original, Cambridge University Press.
[195] Varshalovich, D.A., Moskalev, A.N., Khersonskii, V.K. (1988). Quantum Theory of Angular Momentum, World Scientific Press.
[196] Vielva, P., Martínez-González, E., Gallegos, J. E., Toffolatti, L., Sanz, J. L. (2003) Point source detection using the spherical Mexican hat wavelet on simulated all-sky Planck maps, Monthly Notice of the Royal Astronomical Society, Vol. 344, Issue 1, 89–104.
[197] Vilenkin, N.Ja. and Klimyk, A.U. (1991) Representation of Lie Groups and Special Functions, Kluwer.
[198] Yadav, A.P.S., Komatsu, E., Wandelt, B.D. (2007) Fast estimator of primordial non-Gaussianity from temperature and polarization anisotropies in the Cosmic Microwave Background, Astrophysical Journal, 664:680–686.
[199] Yadav, A.P.S. and Wandelt, B.D. (2008) Evidence of primordial non-Gaussianity (fNL) in the Wilkinson Microwave Anisotropy Probe 3-Year Data at 2.8 sigma, Physical Review Letters, Vol. 100, Issue 18, id. 181301.
[200] Yadav, A.P.S. and Wandelt, B.D. (2010) Primordial non-Gaussianity in the Cosmic Microwave Background, Advances in Astronomy, in press, arXiv: 1006.0275.
[201] Yadrenko, M.I. (1983) Spectral Theory of Random Fields, Translated from the Russian, Translation Series in Mathematics and Engineering, Optimization Software, Inc., Publications Division.
[202] Wiaux, Y., McEwen, J.D., Vielva, P., (2007) Complex data processing: fast wavelet analysis on the sphere, Journal of Fourier Analysis and its Applications, 13, 477–494.
[203] Wiaux, Y., Jacques, L., Vandergheynst, P. (2005) Correspondence principle between spherical and Euclidean wavelets, The Astrophysical Journal, Vol. 632, Issue 1, pp. 15–28.
[204] Wiaux, Y., Jacques, L., Vandergheynst, P. (2007) Fast spin +-2 spherical harmonics transforms and application in cosmology, Journal of Computational Physics, 226:2359–2371.
[205] Wiener, N. (1938), The homogeneous chaos, American Journal of Mathematics, 60, 879–936.
[206] Wigman, I. (2009) On the distribution of the nodal sets of random spherical harmonics, Journal of Mathematical Physics, 50, no. 1, 013521, 44 pp.
[207] Wigman, I. (2010) Fluctuations of the nodal length of random spherical harmonics, Communications in Mathematical Physics, Vol. 298, n. 3, pp. 787–831, arXiv: 0907.1648.
[208] Zaldarriaga, M., Seljak, U. (2000) CMBFAST for spatially closed Universes, Astrophysical Journal Supplements Series, 129, 431–434.