Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T02:01:16.403Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  25 January 2019

Nikolaï Nikolski
Translated by
Danièle Gibbons  and
Greg Gibbons
Nikolaï Nikolski
Affiliation:
Université de Bordeaux
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Hardy Spaces , pp. 259 - 267
Publisher: Cambridge University Press
Print publication year: 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

A

Akhiezer, N. I. (1956), On the weighted approximation of continuous functions by polynomials on the real axis. Uspekhi Mat. Nauk 11:4 ( 70 ), 3–43. English translation: Amer. Math. Soc. Transl. (2) 22 (1962), 95–137.Google Scholar
Akhiezer, N. I. (1965), Lectures on Approximation Theory (in Russian), second edition. Nauka, Moscow. English translation: Approximation Theory, Dover, New York (1992).Google Scholar

B

Báez-Duarte, L. (2003), A strengthening of the Nyman–Beurling criterion for the Riemann hypothesis. Rend. Lincei (9) Mat. Appl. 14, 5–11.Google Scholar
Bagchi, B. (2006), On Nyman, Beurling, and Baez-Duarte’s Hilbert space reformulation of the Riemann hypothesis. Proc. Indian Acad. Sci. (Math. Sci.) 116:2, 137–146.CrossRefGoogle Scholar
Balazard, M. (2010), Un siècle et demi de recherches sur l’hypothèse de Riemann. Gazette des mathématiciens (Soc. Math. France) 126, 7–24.Google Scholar
Banach, S. (1932), Théorie des opérations linéaires. Monografie Matematyczne, Warsaw.Google Scholar
Baranov, A., Belov, Yu. and Borichev, A. (2013), Hereditary completeness for systems of exponentials and reproducing kernels, Adv. in Math. 235, 525–554.Google Scholar
Baranov, A. and Yakubovich, D. (2016), Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators, Adv. in Math. 302, 740–798.Google Scholar
Barbey, K. and König, H. (1977), Abstract Analytic Function Theory and Hardy Algebras. Vol. 593 of Lecture Notes in Mathematics, Springer, Berlin.Google Scholar
Bernstein, S. N. (1924), Le problème de l’approximation des fonctions continues sur tout l’axe réel et l’une de ses applications. Bull. Math. Soc. France 52, 399–410.Google Scholar
Beurling, A. (1945), On the completeness of {ψ(nt)} on L2(0, 1). In The Collected Works of Arne Beurling, vol. 2: Harmonic Analysis. Contemporary Mathematicians, Birkhäuser, Boston (1989), pp. 378–380.Google Scholar
Beurling, A. (1949), On two problems concerning linear transformations in Hilbert space. Acta Math. 81, 79–93.Google Scholar
Blagouchine, Ia. (2018), The history of the ζ functional equation, and the role of different mathematicians in its proof, A seminar talk at POMI seminar on the history of mathematics, March 1, 2018, www.mathnet.ru/php/conference.phtml?optionlang=rus&eventID=10&confid=504.Google Scholar
Blaschke, W. (1915), Eine Erweiterung des Satzes von Vitali über Folgen analytischer Funktionen. S.-B. Sächs Akad. Wiss. Leipzig Math-Natur. Kl. 67, 194–200.Google Scholar
Boas, R. P. (1954), Entire Functions. Academic Press, New York.Google Scholar
Bohr, H. (1913), Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichletschen Reihen Nachr. Ges. Wiss. Göttingen. Math.-Phys. Kl. A9, 441–488.Google Scholar
Borichev, A. (2001), On the closure of polynomials in weighted spaces of functions on the real line. Indiana Univ. Math. J. 50, 829–846.CrossRefGoogle Scholar
Borichev, A. and Sodin, M. (2001), Krein’s entire functions and Bernstein approximation problem. Illinois J. Math. 45:1, 167–185.Google Scholar
Bourgin, D. G. (1946), A class of sequences of functions. Trans. Amer. Math. Soc. 60, 478–518.Google Scholar
Butzer, P. L. (1983), A survey of the Whittaker–Shannon sampling theorem and some of its extensions. J. Math. Res. Exposition 3, 185–212.Google Scholar
Butzer, P. L., Ferreira, P. J. S. G., Higgins, J. R., Saitoh, S., Schmeisser, G., Stens, R. L. (2011), Interpolation and Sampling: E. T. Whittaker, K. Ogura and Their Followers. J. Fourier Analysis Appl. 17:2, 320–354.CrossRefGoogle Scholar
Butzer, P. L., Higgins, J. R., and Stens, R. L. (2000), Sampling theory of signal analysis 1950–1995. In Development of Mathematics 1950–2000 (ed. Pier, J.-P.), Birkhäuser, Basel, pp. 193–234.CrossRefGoogle Scholar

C

Calderón, A. P. (1950), On theorems of M. Riesz and A. Zygmund. Proc. Amer. Math. Soc. 1, 533–535.CrossRefGoogle Scholar
Carleson, L. (1956), Representations of continuous functions. Math. Zeit. 66, 447–451.Google Scholar
Conrey, J. B. (2003), The Riemann hypothesis. Notices Amer. Math. Soc. March 2003, 341–353.Google Scholar
Cotlar, M. and Sadosky, C. (1979), On the Helson–Szegő theorem and a related class of modified Toeplitz kernels. In Harmonic Analysis in Euclidean Spaces, part 1 (ed. Weiss, G. and Wainger, S.), vol. 35 of Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, RI, pp. 387–407.Google Scholar

D

de Branges, L. (1959), The Bernstein problem. Proc. Amer. Math. Soc. 10, 825–832.Google Scholar
Devinatz, A. and Shinbrot, M. (1969), General Wiener–Hopf operators. Trans. Amer. Math. Soc. 145, 467–494.Google Scholar
DeVore, R. A. and Lorentz, G. G. (1993), Constructive Approximation. Springer.Google Scholar
Duoandikoetxea, J. (2001), Fourier Analysis. American Mathematical Society, Providence, RI.Google Scholar
Duren, P. L. (1970), Theory of Hp Spaces. Academic Press, New York.Google Scholar
Fatou, P. (1906), Série trigonométriques et séries de Taylor. Acta Math. 30, 335–400.Google Scholar

F

Fejér, L. and Riesz, F. (1921), Über einige funktionentheoretische Ungleichungen. Math. Zeit. 11, 305–314.Google Scholar
Ford, K. (2002), Vinogradov’s integral and bounds for the Riemann zeta function. Proc. London Math. Soc. (3) 85, 565–633.Google Scholar
Friedrichs, K. O. (1937), On certain inequalities and characteristic value problems for analytic functions and for functions of two variables. Trans. Amer. Math. Soc. 41, 321–364.Google Scholar

G

Gamelin, T. W. (1969), Uniform Algebras. Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
Gantmacher, F. R. (1966), The Theory of Matrices (in Russian), second edition. Nauka, Moscow. English translation: Chelsea, New York (1960).Google Scholar
Garnett, J. B. (1981), Bounded Analytic Functions. Academic Press, New York.Google Scholar
Gelfond, A. O. (1958), Die Rolle der Arbeiten L. Eulers für die Entwicklung der Zahlentheorie (in Russian, with a summary in German). In Leonhard Euler (zu 250. Geburtstages) (ed. Lavrentiev, M., Yushkevich, A., and Grigoriyan, A.), Academy of Sciences of the USSR, Moscow, pp. 96–129.Google Scholar
Glazman, I. M. and Lyubich, Y. I. (1969), Finite-dimensional Linear Analysis (in Russian). Nauka, Moscow. English translation: Finite-dimensional Linear Analysis: A Systematic Presentation in Problem Form, MIT Press, Cambridge, MA (1974).Google Scholar
Golub, G. and Van Loan, C. (1996), Matrix Computations, third edition. Johns Hopkins University Press, Baltimore and London.Google Scholar
Goluzin, G. M. (1966), Geometric Theory of Functions of a Complex Variable (in Russian). Nauka, Moscow. English translation: American Mathematical Society, Providence, RI (1969).Google Scholar
Green, B. and Tao, T. (2008), The primes contain arbitrarily long arithmetic progressions. Ann. of Math. 167:2, 481–547.Google Scholar

H

Hardy, G. H. (1913), A theorem concerning Taylor’s series. Quart. J. Pure Math. 44, 147–160.Google Scholar
Hardy, G. H. (1915), On the mean value of the modulus of an analytic function. Proc. London Math. Soc. (2) 14, 269–277.Google Scholar
Hardy, G. H. (1922), On the integration of Fourier series. Messenger of Math. 51, 186–192.Google Scholar
Hardy, G. H. (1941), Notes on special system of orthogonal functions (IV): The orthogonal functions of Whittaker’s cardinal series. Proc. Cambridge Phil. Soc. 37, 331–348.Google Scholar
Hardy, G. H. and Littlewood, J. E. (1916), Some problems of Diophantine approximation: a remarkable trigonometrical series. Proc. Nat. Acad. USA 2, 583–586.Google Scholar
Hardy, G. H. and Littlewood, J. E. (1926), Some new properties of Fourier constants. Math. Ann. 97, 159–209.Google Scholar
Hardy, G. H. and Wright, E. M. (1938), An Introduction to the Theory of Numbers. Sixth edition, Oxford University Press (2008).Google Scholar
Havin, V. and Jöricke, B. (1994), The Uncertainty Principle in Harmonic Analysis. Springer.Google Scholar
Hedenmalm, H., Lindquist, P., and Seip, K. (1997), A Hilbert space of Dirichlet series and systems of dilated functions in L2 (0, 1). Duke Math. J. 86, 1–37.Google Scholar
Hedenmalm, H., Lindquist, P., and Seip, K. (1999), Addendum to “A Hilbert space of Dirichlet series and systems of dilated functions in L2 (0, 1)”. Duke Math. J. 99, 175–178.Google Scholar
Helson, H. (1964), Lectures on Invariant Subspaces. Academic Press, New York.Google Scholar
Helson, H. and Lowdenslager, D. (1961), Invariant subspaces. In Proc. Intern. Symp. Linear Spaces, Jerusalem, Pergamon Press, Oxford, pp. 251–262.Google Scholar
Helson, H. and Sarason, D. (1967), Past and future. Math. Scand. 21, 5–16.Google Scholar
Helson, H. and Szegő, G. (1960), A problem of prediction theory. Ann. Mat. Pura Appl. 51, 107–138.Google Scholar
Herglotz, G. (1911), Über Potenzreihen mit positiven reellen Teil im Einheitskreise. Berichte Verh. Kgl.-sächs. Gesellsch. Wiss. Leipzig, Math.-Phys. Kl. 63, 501–511.Google Scholar
Higgins, J. R. (1985), Five short stories about the cardinal series. Bull. Amer. Math. Soc. 12:1, 45–89.Google Scholar
Higgins, J. R. (1996), Sampling Theory in Fourier and Signal Analysis: Foundations. Clarendon Press, Oxford, and Oxford University Press, New York.Google Scholar
Higgins, J. R. and Stens, R. L., editors (1999), Sampling Theory in Fourier and Signal Analysis: Advanced Topics. Clarendon Press, Oxford.Google Scholar
Hilbert, D. (1909), Wesen und Ziele einer Analysis der unendlich vielen unabhängigen Variablen. Rend. Cir. Mat. Palermo 27, 59–74.Google Scholar
Hilbert, D. (1912), Gründzüge einer allgemeinen Theorie der linearen Integralgleichungen. Teubner, Leipzig.Google Scholar
Hoffman, K. (1962), Banach Spaces of Analytic Functions. Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
Hollenbeck, B. and Verbitsky, I. (2000), Best constants for the Riesz projection. J. Funct. Analysis 175, 370–392.Google Scholar
Hunt, R., Muckenhoupt, B., and Wheeden, R. L. (1973), Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Amer. Math. Soc. 176, 227– 251.Google Scholar

I

Ibragimov, I. A. and Rozanov, Y. A. (1970), Gaussian Stochastic Processes (in Russian). Nauka, Moscow. English translation: Springer (1978).Google Scholar
Ingham, A. E. (1936), A note on Hilbert’s inequality. J. London Math. Soc. 11, 237–240.Google Scholar

J

Jensen, J. L.. 1899), Sur un nouvel et important théorème de la théorie des fonctions. Acta Math. 22, 219–251.Google Scholar

K

Kac, M. (1966), Can one hear the shape of a drum? Amer. Math. Monthly 73 :4(2), 1–23.Google Scholar
Kahane, J. P. and Katznelson, Y. (1971), Sur le comportement radial des fonctions analytiques. C. R. Acad. Sci. Paris Ser. A–B 227, A718–A719.Google Scholar
Kahane, J.-P. and Lemarié-Rieusset, P. G. (1998), Séries de Fourier et ondelettes. Cassini, Paris.Google Scholar
Kahane, J.-P. and Salem, R. (1963) Ensembles parfaits et séries trigonométriques.Hermann, Paris.Google Scholar
Katznelson, Y. (1976), An Introduction to Harmonic Analysis. Dover, New York.Google Scholar
Kenig, C. E. (1994), Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems. CBMS Conference series no. 83, American Mathematical Society, Providence, RI.Google Scholar
Kolmogorov, A. N. (1925), Sur les fonctions harmoniques conjuguées et les séries de Fourier. Fund. Math. 7, 24–29.Google Scholar
Kolmogorov, A. N. (1941), Stationary sequences in Hilbert space (in Russian). Bull. Moscow Univ. Math. 2:6, 1–40.Google Scholar
Koosis, P. (1966), Weighted polynomial approximation on arithmetic progressions of intervals or points. Acta Math. 116, 223–277.Google Scholar
Koosis, P. (1980), Introduction to Hp Spaces. Cambridge University Press.Google Scholar
Kotelnikov, V. A. (1933), On the transmission capacity of “aether” and wire in electro-communications (in Russian). Izdat. Red. Upr. Svyazi RKKA. English translation: http://ict.open.ac.uk/classics/1.pdf.Google Scholar
Kotelnikov, V. A. (1956), The Theory of Optimum Noise Immunity. McGraw-Hill (1959). Russian original: Izdat. Radio i Svyaz’, Moscow.Google Scholar
Kozlov, V. Y. (1948), On the completeness of systems of functions {φ(nx)} in the space L2(0, 2π) (in Russian). Doklady Akad. Nauk SSSR 61, 977–980.Google Scholar
Kozlov, V. Y. (1950), On the completeness of a system of functions of type {φ(nx)} in the space L2 (in Russian). Doklady Akad. Nauk SSSR 73, 441–444.Google Scholar

L

Landau, E. (1927), Vorlesungen über Zahlentheorie, vols 1–3. Hirzel, Leipzig.Google Scholar
Lax, P. D. and Phillips, R. S. (1967), Scattering Theory. Academic Press, New York and London.Google Scholar
Levin, B. Y. (1956), Distribution of Zeros of Entire Functions (in Russian). GITTL, Moscow. English translation: American Mathematical Society, Providence, RI (1980).Google Scholar
Levinson, N. (1956), On the closure problems and the zeros of the Riemann zeta-function. Proc. Amer. Math. Soc. 7, 838–845.Google Scholar
Lindenstrauss, J. and Tzafriri, L. (1977), Classical Banach Spaces, vols I (1977) and II (1979). Springer.Google Scholar
Littlewood, J. E. (1925), On inequalities in the theory of functions. Proc. London Math. Soc. 23, 481–519.Google Scholar
Littlewood, J. E. (1953), A Mathematician’s Miscellany. Methuen, London. Revised edition, Littlewood’s Miscellany (ed. B. Bollobás), Cambridge University Press (1986).Google Scholar
Littlewood, J. E. (1970), The “pits effect” for functions in the unit circle. J. Analyse Math. 23, 237–268.Google Scholar

M

Makino, T., (2003), The Mathematician K. Ogura and the “Greater East Asia War”. In Mathematics and War (ed. B. Booß-Bavnbek and J. Høyrup), Springer, pp. 326–335.Google Scholar
Masani, P. (1966), Wiener’s contribution to generalized harmonic analysis, prediction theory and filter theory. Bull. Amer. Math. Soc. 72 :1(2), 73–125.Google Scholar
McCarthy, C. A. and Schwartz, J. (1965), On the norm of a finite Boolean algebra of projections and applications to theorems of Kreiss and Morton. Comm. Pure Appl. Math. 18, 191–201.Google Scholar
McGehee, O. C., Pigno, L., and Smith, B. (1981), Hardy’s inequality and the L1-norm of exponential sums. Ann. of Math. 113, 613–618.Google Scholar
Mergelyan, S. N. (1956), Weighted approximation by polynomials (in Russian). Uspekhi Mtem. Nauk 11:5, 107–152. English translation: AMS Transl. Ser. 2 10 (1958), 59–106.Google Scholar
Meyer, Y. (1992), Wavelets and Operators. Cambridge University Press.Google Scholar

N

Nehari, Z. (1957), On bounded bilinear forms. Ann. of Math. 65, 153–162.Google Scholar
Neuwirth, J. H., Ginsberg, J., and Newman, D. J. (1970), Approximation by f (kx). J. Funct. Anal. 5, 194–203.Google Scholar
Neuwirth, J. H. and Newman, D. J. (1967), Positive H1/2 functions are constant. Proc. Amer. Math. Soc. 18, 958.Google Scholar
Nevanlinna, F. and Nevanlinna, R. (1922), Über die Eigenschaften analytischer Functionen in der Umgebung einer singulären Stelle oder Linie. Acta Soc. Sci. Fenn. 50:5, 1–46.Google Scholar
Nikolski, N. (1980), Lekzii ob Operatore Sdviga (in Russian). Nauka, Moscow.Google Scholar
Nikolski, N. (1986), Treatise on the Shift Operator. Springer.Google Scholar
Nikolski, N. (1995), Distance formulae and invariant subspaces, with an application to localization of zeros of the Riemann ζ-function. Ann. Inst. Fourier 45:1, 143–159.Google Scholar
Nikolski, N. (2002), Operators, Functions, and Systems, vols 1 and 2. American Mathematical Society, Providence, RI.Google Scholar
Nikolski, N. (2012), In a shadow of the RH: cyclic vectors of Hardy spaces on the Hilbert multidisc. Ann. Inst. Fourier 62:5, 1601–1626.Google Scholar
Nikolski, N. and Volberg, A. (1990), Tangential and approximate free interpolation. In Analysis and Partial Differential Equations (ed. Sadosky, C.), Marcel Dekker, New York, pp. 277–299.Google Scholar
Nyman, B. (1950), On the one-dimensional translation group and semi-group in certain function spaces. Thesis, Uppsala University.Google Scholar

O

Ogura, K. (1920), On a certain transcendental integral function in the theory of interpolation. Tôhoku Math. J. 17, 64–72.Google Scholar
Øksendal, B. K. (1971), A short proof of the F. and M. Riesz theorem. Proc. Amer. Math. Soc. 30, 204.Google Scholar

P

Paley, R. E. A. C. and Wiener, N. (1934), Fourier Transforms in the Complex Domain.Vol. 19 of American Mathematical Society Colloquium Publications, Providence, RI.Google Scholar
Papoulis, A. (1984), Signal Analysis. McGraw-Hill.Google Scholar
Pavlović, M. (2004), Introduction to Function Spaces on the Disk. Matematički Institut SANU, Belgrade.Google Scholar
Peller, V. V. (2003), Hankel Operators and their Applications. Springer.Google Scholar
Peller, V. V. and Khruschev, S. V. (S. V. Hruschev) (1982), Hankel operators, best approximations and stationary Gaussian processes (in Russian). Uspekhi Mat. Nauk 37:1, 53–124. English translation: Russian Math. Surveys 37:1 (1982), 61–144.Google Scholar
Pérez-Marco, R. (2011), Notes on the Riemann hypothesis. In Jornadas sobre los problemas del milenio, Barcelona 1–3 junio, 2011.Google Scholar
Phragmén, E. and Lindelöf, E. (1908), Sur une extension d’un principe classique de l’analyse. Acta Math. 31, 381–406.Google Scholar
Plessner, A. I. (1927), Über das Verhalten analytischer Funktionen am Rande ihres Definitionsbereichs. J. Reine Angew. Math. 158, 219–227.Google Scholar
Pólya, G. and Szegő, G. (1925), Aufgaben und Lehrsätze aus der Analysis, vols 1, 2. Springer, Berlin. English translation: Springer (1972).Google Scholar
Power, S. C. (1982), Hankel Operators on Hilbert Space. Vol. 64 of Pitman Research Notes in Mathematics, Pitman.Google Scholar
Privalov, I. I. (1941), Boundary Properties of Analytic Functions (in Russian). Moscow (second edition 1950). German translation: Deutscher Verlag, Berlin (1956).Google Scholar

R

Reid, C. (1970), Hilbert. Springer, New York.Google Scholar
Riesz, F. (1923), Über die Randwerte einer analytische Funktion. Math. Z. 18, 87–95.Google Scholar
Riesz, F. and Riesz, M. (1916), Über die Randwerte einer analytische Funktion. In Quatrième Congrès des Math. Scand., Stockholm, pp. 27–44.Google Scholar
Riesz, F. and Szőkefalvi-Nagy, B. (1955), Leçons d’analyse fonctionnelle. Akadémiai Kiado, Szeged.Google Scholar
Riesz, M. (1927), Sur les fonctions conjuguées. Math. Zeit. 27, 218–244.Google Scholar
Rosenblum, M. (1962), Summability of Fourier series in Lp(μ). Trans. Amer. Math. Soc. 105:1, 32–42.Google Scholar
Rozanov, Y. A. (1963), Stationary Stochastic Processes (in Russian). Fizmatgiz, Moscow. English translation: Holden-Day, San Francisco (1967).Google Scholar
Rudin, W. (1956), Boundary values of continuous analytic functions. Proc. Amer. Math. Soc. 7, 808–811.Google Scholar
Rudin, W. (1962), Fourier Analysis on Groups. Wiley, New York.Google Scholar
Rudin, W. (1998), Analyse réelle et complexe, third edition. Dunod, Paris.Google Scholar

S

Sabbagh, K. (2002), The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics. Farrar, Straus and Giroux, New York.Google Scholar
Salem, R. (1953), Sur une proposition équivalente à l’hypothèse de Riemann. C. R. Acad. Sci. Paris 236, 1127–1128.Google Scholar
Sarason, D. (1994), Sub-Hardy Hilbert Spaces in the Unit Disk. University of Arkansas Lecture Notes, no. 10, Wiley, New York.Google Scholar
Shannon, C. E. (1948), A mathematical theory of communication. Bell System Technical Journal 27, July and October, 379–423 and 623–656.Google Scholar
Shannon, C. E. (1949), Communication theory of secrecy systems. Bell System Technical Journal 28, October, 656–715.Google Scholar
Shannon, C. E. (1950), Programming a computer for playing chess. Philosophical Magazine (7) 41:314, 256–275.Google Scholar
Shapiro, J. H. (1993), Composition Operators and Classical Function Theory. Springer, New York.Google Scholar
Simon, B. (2005), Orthogonal Polynomials on the Unit Circle, Part 1: Classical Theory. American Mathematical Society, Providence, RI.Google Scholar
Smirnov, V. I. (1928a), Sur la théorie des polynômes orthogonaux à une variable complexe. J. Leningrad Fiz.-Mat. Obsch. 2:1, 155–179.Google Scholar
Smirnov, V. I. (1928b), Sur les valeurs limites des fonctions régulières à l’intérieur d’un cercle. J. Leningrad Fiz.-Mat. Obsch. 2:2, 22–37.Google Scholar
Smirnov, V. I. (1932), Sur les formules de Cauchy et Green et quelques problèmes qui s’y rattachent. Izvestia AN SSSR, ser. fiz.-mat. 3, 338–372.Google Scholar
Smirnov, V. I. (1988), Œuvres choisies: Analyse complexe et théorie de diffusion (in Russian). University of Leningrad.Google Scholar
Spijker, M. N., Tracogna, S., and Welfert, B. (2003), About the sharpness of the stability estimates in the Kreiss matrix theorem. Math. Comp. 72, 697–713.Google Scholar
Srinivasan, T. P. (1963), Simply invariant subspaces. Bull. Amer. Math. Soc. 69, 706–709.Google Scholar
Steele, J. M. (2004), The Cauchy–Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities. Cambridge University Press.Google Scholar
Stein, E. (1993), Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton, New Jersey.Google Scholar
Szegő, G. (1920), Beiträge zur Theorie der Toeplitzsche Formen, I. Math. Zeit. 6:3/4, 167–202.Google Scholar
Szegő, G. (1921), Über die Randwerte einer analytischen Funktion. Math. Ann. 84:3/4, 232–244.Google Scholar

T

Thomson, J. E. (1991), Approximation in the mean by polynomials. Ann. of Math. (2), 133:3, 477–507.Google Scholar
Titchmarsh, E. C. (1939), The Theory of Functions. Oxford Science Publications.Google Scholar
Titchmarsh, E. C. (1951), The Theory of the Riemann Zeta-function. Oxford Science Publications.Google Scholar
Tsereteli, O. D. (1975), Metric properties of conjugate functions (in Russian). Itogi Nauki i Techniki Sovrem. Probl. Mat. 7, 18–57. English translation: J. Soviet Math. 7 (1977), 309–414.Google Scholar

V

Verblunsky, S. (1936), On positive harmonic functions (second paper). Proc. London Math. Soc. (2) 40, 290–320.Google Scholar
von Koch, H. (1902), Ueber die Riemann’sche Primzahlfunction. Math. Annalen 55, 441–464. WGoogle Scholar

W

Weyl, H. (1908), Singuläre Integralgleichungen. Math. Ann. 66, 273–324.Google Scholar
Whittaker, E. T. (1915), On the functions which are represented by the expansions of the interpolation theory. Proc. Royal Soc. Edinburgh Ser. A 35, 181–194.Google Scholar
Whittaker, E. T. (1924), The Calculus of Observations: A Treatise on Numerical Mathematics. Blackie, London.Google Scholar
Wiener, N. (1930), Generalized harmonic analysis. Acta Math. 55, 117–258.Google Scholar
Wiener, N. (1932), Tauberian theorems. Ann. of Math. (2) 33, 1–100.Google Scholar
Wiener, N. (1933), The Fourier Integral and Certain of its Applications. Cambridge University Press, New York.Google Scholar
Wiener, N. (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications. MIT Press, Cambridge, MA, and Wiley, New York.Google Scholar
Wiener, N. and Masani, P. R. (1957), The prediction theory of multivariate stochastic processes, I: The regularity condition. Acta Math. 98, 111–150.Google Scholar
Wiener, N. and Masani, P. R. (1958), The prediction theory of multivariate stochastic processes, II: The linear predictor. Acta Math. 99, 93–137.Google Scholar
Wintner, A. (1944), Diophantine approximation and Hilbert’s space. Amer. J. Math. 66, 564–578.Google Scholar
Wold, H. (1938), A Study in the Analysis of Stationary Time Series. Almquist och Wiksell, Uppsala.Google Scholar

Z

Zygmund, A. (1959), Trigonometric Series, vols I and II. Cambridge University Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×