Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Michael B. Marcus and Gilles Pisier
Title: Random Fourier series with applications to harmonic analysis
Additional book information: Annals of Mathematics Studies, No. 101, Princeton Univ. Press, Princeton, N.J., 1981, v + 150 pp., $17.50 (cloth), $7.00 (paperback).

References [Enhancements On Off] (What's this?)

  • 1. R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Funct. Anal. 1 (1967), 290-330. MR 220340
  • 2. X. Fernique, Des résultats nouveaux sur les processus gaussien, C. R. Acad. Sci. Paris Sér. A 278 (1974), 363-365. MR 413237
  • 3. G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc. 71 (1951), 38-69. MR 51340
  • 4. N. C. Jain and M. B. Marcus, Continuity of sub-gaussian processes, Advances in Probability, vol. 4, Dekker, New York, 1978. MR 515431
  • 5. J. P. Kahane, Some random series of functions, D. C. Heath, Lexington, Mass., 1968. MR 254888
  • 6. M. B. Marcus and G. Pisier, Necessary and sufficient conditions for the uniform convergence of random trigonometric series, Lecture Note Series, no. 50, Arhus University, Arhus, Denmark, 1978. MR 507061
  • 7. M. B. Marcus and G. Pisier, Random Fourier series on locally compact Abelian groups, Séminarie de Probabilities XIII (Université de Strasbourg 1977/1978), Lecture Notes in Math., vol. 709, Springer-Verlag, Berlin and New York, 1979, pp. 72-89. MR 544781
  • 8. R. E. A. C. Paley and A. Zygmund, On some series of functions. (1), (2), (3), Proc. Cambridge Philos. Soc. 26(1930), 337-357; 26(1930), 458-474; 28(1932), 190-205.
  • 9. G. Pisier, Sur l'espace de Banach des séries de Fourier aléatoires presque sûrement continues, Exposé No. 17-18, Séminaire sur la géométrie des espace de Banach (1977-78), École Polytechnique, Palaiseau. MR 520216
  • 10. G. Pisier, Ensembles de Sidon et processus gaussiens, C. R. Acad. Sci. Paris Sér. A 286 (1978), 671-674. MR 511046
  • 11. D. Rider, Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), 759-764. MR 387965
  • 12. W. Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-227. MR 116177

Review Information:

Reviewer: Daniel Rider
Journal: Bull. Amer. Math. Soc. 8 (1983), 353-356
American Mathematical Society