Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T23:44:43.209Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Radon Transform and Lévy’s Brownian Motion, II*)

Published online by Cambridge University Press:  22 January 2016

Akio Noda
Akio Noda*
Affiliation:
Department of Mathematics Aichi University of Education, Kariya 448, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

As a continuation of the author’s paper, we shall investigate the null spaces of a dual Radon transform R*, in connection with a Lévy’s Brownian motion X with parameter space (Rn, d). We shall follow the notation used in (I).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 89 - 107
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

Footnotes

*)

Contribution to the research project Reconstruction, Ko 506/8-1, of the German Research Council (DFG), directed by Professor D. Kölzow, Erlangen.

References

[ 1 ] Ambartzumian, R. V., Combinatorial integral geometry, with applications to mathematical stereology, John Wiley & Sons, Chichester, 1982.Google Scholar
[ 2 ] Assouad, P., Produit tensoriel, distances extrémales et realisation de covariance, I et II, C. R. Acad. Sci. Paris Ser. A, 288 (1979), 649–652 et 675–677.Google Scholar
[ 3 ] Assouad, P. et Deza, M., Espaces métriques plongeables dans un hypercube: Aspects combinatories, Ann. Discrete Math., 8 (1980), 197–210.CrossRefGoogle Scholar
[ 4 ] Berg, C., Christensen, J. P. R. and Ressel, P., Harmonic analysis on semigroups, Springer-Verlag, New York, 1984.Google Scholar
[ 5 ] Bolker, E. D., A class of convex bodies, Trans. Amer. Math. Soc, 145 (1969), 323–345.Google Scholar
[ 6 ] Bretagnolle, J., Dacunha-Castelle, D. et Krivine, J. L., Lois stables et espaces LP Ann. Inst. H. Poincarè Sect. B, 2 (1966), 231–259.Google Scholar
[ 7 ] Chentsov, N. N., Levy Brownian motion for several parameters and generalized white noise, Theory Probab. Appl., 2 (1957), 265–266 (English translation).CrossRefGoogle Scholar
[ 8 ] Choquet, G., Lectures on analysis, Vol. III, W. A. Benjamin, New York, 1969.Google Scholar
[ 9 ] Deans, S. R., The Radon transform and some of its applications, John Wiley & Sons, New York, 1983.Google Scholar
[10] Dor, L. E., Potentials and isometric embeddings in Li, Israel J. Math., 24 (1976), 260–268.Google Scholar
[11] Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G., Higher transcendental functions (Bateman manuscript project), Vol. II, McGraw-Hill, New York, 1953.Google Scholar
[12] Helgason, S., The Radon transform, Birkhäuser, Boston, 1980.Google Scholar
[13] Hida, T., Kei-Seung, Lee and Sheu-San, Lee, Conformal invariance of white noise, Nagoya Math. J., 98 (1985), 87–98.CrossRefGoogle Scholar
[14] Levy, P., Théorie de l’addition des variables aléatoires, Gauthier-Villars, Paris, 1954.Google Scholar
[15] Levy, P., Processus stochastiques et mouvement brownien, Gauthier-Villars, Paris, 1965.Google Scholar
[16] Ludwig, D., The Radon transform on Euclidean space, Comm. Pure Appl. Math., 19 (1966), 49–81.Google Scholar
[17] McKean, H. P., Brownian motion with a several-dimensional time, Theory Probab. Appl., 8 (1963), 335–354.Google Scholar
[18] Noda, A., Lévy’s Brownian motion; Total positivity structure of M(¿)-process and deterministic character, Nagoya Math. J., 94 (1984), 137–164.Google Scholar
[19] Noda, A., Generalized Radon transform and Lévy’s Brownian motion, I, Nagoya Math. J., 105 (1987), 71–87.Google Scholar
[20] Quinto, E. T., Null spaces and ranges for the classical and spherical Radon transforms, J. Math. Anal. Appl., 90 (1982), 408–420.Google Scholar
[21] Quinto, E. T., Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform, J. Math. Anal. Appl., 95 (1983), 437–448.Google Scholar
[22] Strichartz, R. S., Radon inversion—variations on a theme, Amer. Math. Monthly, 89 (1982), 377–384 and 420–423.Google Scholar
[23] Takenaka, S., Kubo, I. and Urakawa, H., Brownian motion parametrized with metric spaces of constant curvature, Nagoya Math. J., 82 (1981), 131–140.Google Scholar
[24] Takenaka, S., Representation of Euclidean random field, Nagoya Math. J., 105 (1987),19–31.Google Scholar
[25] Yaglom, A. M., Some classes of random fields in n-dimensional space related to stationary random processes, Theory Probab. Appl., 2 (1957), 273–320.Google Scholar
[26] Zalcman, L., Offbeat integral geometry, Amer. Math. Monthly, 87 (1980), 161–175.Google Scholar