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Bulletin of the American Mathematical Society

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Book Review

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Full text of review: PDF
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?)

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  • 2. Xavier Fernique, Des résultats nouveaux sur les processus gaussiens, C. R. Acad. Sci. Paris Sér. A 278 (1974), 363–365 (French). MR 0413237
  • 3. G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc. 71 (1951), 38–69. MR 0051340, 10.1090/S0002-9947-1951-0051340-3
  • 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. Jean-Pierre Kahane, Some random series of functions, D. C. Heath and Co. Raytheon Education Co., Lexington, Mass., 1968. MR 0254888
  • 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. Gilles Pisier, Ensembles de Sidon et processus gaussiens, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 15, A671–A674 (French, with English summary). MR 0511046
  • 11. Daniel Rider, Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), no. 4, 759–764. MR 0387965
  • 12. Walter Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227. MR 0116177

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