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Book Review

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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. Naresh C. Jain and Michael B. Marcus, Continuity of sub-Gaussian processes, Probability on Banach spaces, Adv. Probab. Related Topics, vol. 4, Dekker, New York, 1978, pp. 81–196. 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 Notes Series, vol. 50, Aarhus Universitet, Matematisk Institut, Aarhus, 1978. Lecture 1977/78. MR 507061
  • 7. M. B. Marcus and G. Pisier, Random Fourier series on locally compact abelian groups, Séminaire de Probabilités, XIII (Univ. Strasbourg, Strasbourg, 1977/78), Lecture Notes in Math., vol. 721, Springer, Berlin, 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, Séminaire sur la Géométrie des Espaces de Banach (1977–1978), École Polytech., Palaiseau, 1978, pp. Exp. No. 17–18, 33 (French). 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
DOI: https://doi.org/10.1090/S0273-0979-1983-15119-4
American Mathematical Society