Bulletin of the American Mathematical Society

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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).

R. M. Dudley, The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional Analysis 1 (1967), 290–330. MR 0220340, DOI 10.1016/0022-1236(67)90017-1

Xavier Fernique, Des résultats nouveaux sur les processus gaussiens, C. R. Acad. Sci. Paris Sér. A 278 (1974), 363–365 (French). MR 413237

G. A. Hunt, Random Fourier transforms, Trans. Amer. Math. Soc. 71 (1951), 38–69. MR 51340, DOI 10.1090/S0002-9947-1951-0051340-3

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

Jean-Pierre Kahane, Some random series of functions, D. C. Heath and Company Raytheon Education Company, Lexington, Mass., 1968. MR 0254888

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

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.

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

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 511046

Daniel Rider, Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), no. 4, 759–764. MR 387965

Walter Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227. MR 0116177, DOI 10.1512/iumj.1960.9.59013

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 0220340

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