Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
Séminaire d'analyse fonctionnelle (1979-1980), Exposé no. 13 et 14, 43 p. 
@article{SAF_1979-1980____A11_0,
     author = {Pisier, G.},
     title = {Conditions d'entropie assurant la continuit\'e de certains processus et applications \`a l'analyse harmonique},
     journal = {S\'eminaire d'analyse fonctionnelle},
     note = {talk:13 et 14},
     pages = {1--43},
     year = {1979-1980},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     zbl = {0441.60040},
     language = {fr},
     url = {https://www.numdam.org/item/SAF_1979-1980____A11_0/}
}
TY  - JOUR
AU  - Pisier, G.
TI  - Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
JO  - Séminaire d'analyse fonctionnelle
N1  - talk:13 et 14
PY  - 1979-1980
SP  - 1
EP  - 43
PB  - Ecole Polytechnique, Centre de Mathématiques
UR  - https://www.numdam.org/item/SAF_1979-1980____A11_0/
LA  - fr
ID  - SAF_1979-1980____A11_0
ER  - 
%0 Journal Article
%A Pisier, G.
%T Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
%J Séminaire d'analyse fonctionnelle
%Z talk:13 et 14
%D 1979-1980
%P 1-43
%I Ecole Polytechnique, Centre de Mathématiques
%U https://www.numdam.org/item/SAF_1979-1980____A11_0/
%G fr
%F SAF_1979-1980____A11_0
Pisier, G. Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique. Séminaire d'analyse fonctionnelle (1979-1980), Exposé no. 13 et 14, 43 p.. https://www.numdam.org/item/SAF_1979-1980____A11_0/

[1] P. Assouad: Factorisation des applications Λp-sommantes, Séminaire Maurey-Schwartz 1973-74, exposé No 11. | Numdam

[2] P. Boulicaut: Fonctions de Young et continuité des trajectoires d'une fonction aléatoire, Annales de l'Institut Fourier, 24, 2 (1974), 27-47. | Zbl | MR | Numdam

[3] B. Carl: Entropy numbers, s-numbers and eigenvalue problems, à paraître. | Zbl

[4] B. Carl et H. Triebel: Inequalities between eigenvalues, entropy numbers and related quantities of compact operators in Banach spaces, à paraître. | Zbl

[5] K.M. Chong et N.M. Rice: Equimeasurable rearrangements of functions, Queens Papers in Pure and Applied Maths. No 28, Queens Univetsity 1971. | Zbl | MR

[6] P. De Land: Moduli of continuity for exponential Lipschitz classes, TAMS 229 (1977) 175-189. | Zbl | MR

[7] J. Delporte: Fonctions aléatoires presque sûrement continues sur un intervalle fermé, Ann. Inst. H. Poincaré Sér. B 1 (1964), 111-215. | Zbl | MR | Numdam

[8] R.M. Dudley: Sample functions of the Gaussian process, Annals of Probability 1 (1973) 66-103. | Zbl | MR

[9] R.M. Dudley: The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional. Analysis 1 (1967) 290-330. | Zbl | MR

[10] N. Dunford, J. Schwartz: Linear operators, Part II, Wiley Interscience 1963. | Zbl | MR

[11] X. Fernique: Régularité des trajectoires des fonctions aléatoires gaussiennes, Ecole d'Eté de Saint Flour (1974), Springer Lecture Notes in Maths. No 480. | Zbl | MR

[12] X. Fernique: Continuité des processus gaussiens, C. R. Acad. Sc. Paris, A 258 (1964) 6058-6060. | Zbl | MR

[13] A. Garsia: A remarkable inequality and the uniform convergence of Fourier series, Indiana Univ. Math. Journal 25 (1976) 85-102. | Zbl | MR

[14] A.M. Garsia et E. Rodemich: Monotonicity of certain functionals under rearrangement, Annales de l'Institut Fourier 24, 2 (1974), 67-116. | Zbl | MR | Numdam

[15] A. Garsia, E. Rodemich et H. Rumsey Jr.: A real variable lemma and the continuity of paths of Gaussian processes, Indiana Univ. Math. Journal 20 (1970) 565-578. | Zbl | MR

[16] A. Garsia: Combinatorial inequalities and smoothness of functions, Bull. A.M.S. 82 (1976) 157-170. | Zbl | MR

[17] M.G. Hahn: Central limit theorems for D([0,1])-valued random variables, Ph. D Thesis, M.I.T. Cambridge 1975.

[18] M.G. Hahn: Conditions for sample continuity and the central limit theorem, Annals of Probability 5 (1977) 351-360. | Zbl | MR

[19] M.G. Hahn:: A note on the central limit theorem of square integrable processes, Proc. A.M.S. 64 (1977) 331-334. | Zbl | MR

[20] M.G. Hahn et M.J. Klass: Sample continuity of square integrable prucesses, Annals of Probability 5 (1977) 361-370. | Zbl | MR

[21] C.S. Herz: Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transform, J. Math. Mech. 18 (1968) 283-324. | Zbl | MR

[22] J. Hoffmann-Jørgensen et G. Pisier: The law of large numbers and the central limit theorem in Banach spaces, Annals of Probability 4 (1976) 587-599. | Zbl | MR

[23] I. Ibragimov: Properties of sample functions for stochastic processes and embedding theorems, Theory of Probability and its Appl, 18 (1973) 442-453. | Zbl

[24] I. Ibragimov: Sur la régularité des trajectoires des fonctions aléatoires, C. R. Acad. Sc. Paris A 289 (1979) 545-547. | Zbl | MR

[25] N. Jain et M.B. Marcus: Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series series of functions, Annales Inst. Fourier 24, 2 (1974) 117-141. | Zbl | MR | Numdam

[26] J.P. Kahane: Séries de Fourier absolument convergentes, Springer Verlag (1970), Ergebnisse Band 50. | Zbl | MR

[27] N. Kôno: Best possibility of an integral test for sample continuity of L P-processes (p ≽ 2), Proc. Japan Acad. 54 ser. A (1978) 197-201. | Zbl

[28] M. Loeve: Probability theory, Van Nostrand, 3ème édition, 1963. | Zbl | MR

[29] G.G. Lorentz: Approximation of functions, Holt, Rinehart and Winston, New-York 1966. | Zbl | MR

[30] G.G. Lorentz: Metric entropy and approximation, Bull. A.M.S. 72 (1966) 903-937. | Zbl | MR

[31] M.B. Marcus et G. Pisier: Random Fourier series with applications to harmonie analysis, preprint.

[32] M.B. Marcus et L.A. Shepp: Sample behavior of Gaussian processes, Sixth Berkeley Symposium (1970) p. 423-441. | Zbl | MR

[33] M.B. Marcus et L.A. Shepp: Continuity of Gaussian processes, Trans. A.M.S. 151 (1970) 377-391. | Zbl | MR

[34] C. Nanopoulos et P. Nohelis: Etude de la régularité et des propriétés limites des fonctions aléatoires définies sur [0,1]n, de type puissance. C. R. Acad. Sc. Paris A 285 (1977) 273-276. | Zbl | MR

[35] C. Nanopoulos et P. Nobelis: Etude de la régularité des fonctions aléatoires et de leurs propriétés limites, Thèse de 3ème cycle (1977) Université de Strasbourg.

[36] T.W. Park: Sobolev type inequalities and path continuity of L p processes with multidimensional time parameter, Ph. D. Thesis.

[37] A. Pietsch: Operator ideals, Berlin, 1978. | Zbl | MR

[38] A. Pietsch: Weyl numbers and eigenvalues of operators in Banach spaces, Math. Annalen (1980). | Zbl | MR

[39] C. Preston: Banach spaces arising from some integral inequalities, Indiana University Math. Journal 20 (1971) 997-1015. | Zbl | MR

[40] C. Preston: Continuity properties of some Gaussian processes, Annals of Math. Stat. 43 (1972) 285-292. | Zbl | MR

[41] Séminaire L. Schwartz sur les applications radonifiantes 1969-70, Ecole Polytechnique, Paris. | Zbl

[42] Séminaire Maurey-Schwartz 1973-74, Ecole Polytechnique, Paris.

[43] J.H. Wells et L.R. Williams: Embeddings and extensions in analysis, Springer Verlag (1975), Ergebnisse Band 84. | Zbl | MR