Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1979-1980)
- page 1-43
Access Full Article
topHow to cite
topPisier, G.. "Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique." Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1979-1980): 1-43. <http://eudml.org/doc/109222>.
@article{Pisier1979-1980,
author = {Pisier, G.},
journal = {Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")},
keywords = {central limit theorem; law of iterated logarithm; sample continuity; metric entropy; p-summing operator; absolutely convergent Fourier series; approximation numbers},
language = {fre},
pages = {1-43},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique},
url = {http://eudml.org/doc/109222},
year = {1979-1980},
}
TY - JOUR
AU - Pisier, G.
TI - Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
JO - Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
PY - 1979-1980
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 43
LA - fre
KW - central limit theorem; law of iterated logarithm; sample continuity; metric entropy; p-summing operator; absolutely convergent Fourier series; approximation numbers
UR - http://eudml.org/doc/109222
ER -
References
top- [1] P. Assouad: Factorisation des applications Λp-sommantes, Séminaire Maurey-Schwartz 1973-74, exposé No 11.
- [2] P. Boulicaut: Fonctions de Young et continuité des trajectoires d'une fonction aléatoire, Annales de l'Institut Fourier, 24, 2 (1974), 27-47. Zbl0275.60051MR458563
- [3] B. Carl: Entropy numbers, s-numbers and eigenvalue problems, à paraître. Zbl0466.41008
- [4] B. Carl et H. Triebel: Inequalities between eigenvalues, entropy numbers and related quantities of compact operators in Banach spaces, à paraître. Zbl0465.47019
- [5] K.M. Chong et N.M. Rice: Equimeasurable rearrangements of functions, Queens Papers in Pure and Applied Maths. No 28, Queens Univetsity1971. Zbl0275.46024MR372140
- [6] P. De Land: Moduli of continuity for exponential Lipschitz classes, TAMS229 (1977) 175-189. Zbl0349.26004MR442157
- [7] J. Delporte: Fonctions aléatoires presque sûrement continues sur un intervalle fermé, Ann. Inst. H. Poincaré Sér.B1 (1964), 111-215. Zbl0138.10701MR183011
- [8] R.M. Dudley: Sample functions of the Gaussian process, Annals of Probability1 (1973) 66-103. Zbl0261.60033MR346884
- [9] R.M. Dudley: The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. Functional. Analysis1 (1967) 290-330. Zbl0188.20502MR220340
- [10] N. Dunford, J. Schwartz: Linear operators, Part II, Wiley Interscience1963. Zbl0128.34803MR1009163
- [11] X. Fernique: Régularité des trajectoires des fonctions aléatoires gaussiennes, Ecole d'Eté de Saint Flour (1974), Springer Lecture Notes in Maths. No 480. Zbl0331.60025MR413238
- [12] X. Fernique: Continuité des processus gaussiens, C. R. Acad. Sc. Paris, A258 (1964) 6058-6060. Zbl0129.30101MR164365
- [13] A. Garsia: A remarkable inequality and the uniform convergence of Fourier series, Indiana Univ. Math. Journal25 (1976) 85-102. Zbl0324.42005MR413247
- [14] A.M. Garsia et E. Rodemich: Monotonicity of certain functionals under rearrangement, Annales de l'Institut Fourier24, 2 (1974), 67-116. Zbl0274.26006MR414802
- [15] A. Garsia, E. Rodemich et H. RumseyJr.: A real variable lemma and the continuity of paths of Gaussian processes, Indiana Univ. Math. Journal20 (1970) 565-578. Zbl0252.60020MR267632
- [16] A. Garsia: Combinatorial inequalities and smoothness of functions, Bull. A.M.S.82 (1976) 157-170. Zbl0351.26005MR582776
- [17] M.G. Hahn: Central limit theorems for D([0,1])-valued random variables, Ph. D Thesis, M.I.T.Cambridge1975.
- [18] M.G. Hahn: Conditions for sample continuity and the central limit theorem, Annals of Probability5 (1977) 351-360. Zbl0388.60043MR440679
- [19] M.G. Hahn:: A note on the central limit theorem of square integrable processes, Proc. A.M.S.64 (1977) 331-334. Zbl0334.60013MR448487
- [20] M.G. Hahn et M.J. Klass: Sample continuity of square integrable prucesses, Annals of Probability5 (1977) 361-370. Zbl0388.60044MR440680
- [21] C.S. Herz: Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transform, J. Math. Mech.18 (1968) 283-324. Zbl0177.15701MR438109
- [22] J. Hoffmann-Jørgensen et G. Pisier: The law of large numbers and the central limit theorem in Banach spaces, Annals of Probability4 (1976) 587-599. Zbl0368.60022MR423451
- [23] I. Ibragimov: Properties of sample functions for stochastic processes and embedding theorems, Theory of Probability and its Appl, 18 (1973) 442-453. Zbl0324.60033
- [24] I. Ibragimov: Sur la régularité des trajectoires des fonctions aléatoires, C. R. Acad. Sc. ParisA289 (1979) 545-547. Zbl0416.60043MR557270
- [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. Fourier24, 2 (1974) 117-141. Zbl0283.60041MR413239
- [26] J.P. Kahane: Séries de Fourier absolument convergentes, Springer Verlag (1970), Ergebnisse Band 50. Zbl0195.07602MR275043
- [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. Zbl0407.60039
- [28] M. Loeve: Probability theory, Van Nostrand, 3ème édition, 1963. Zbl0108.14202MR203748
- [29] G.G. Lorentz: Approximation of functions, Holt, Rinehart and Winston, New-York1966. Zbl0153.38901MR213785
- [30] G.G. Lorentz: Metric entropy and approximation, Bull. A.M.S.72 (1966) 903-937. Zbl0158.13603MR203320
- [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. Zbl0379.60040MR402896
- [33] M.B. Marcus et L.A. Shepp: Continuity of Gaussian processes, Trans. A.M.S.151 (1970) 377-391. Zbl0209.49201MR264749
- [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. ParisA285 (1977) 273-276. Zbl0366.60057MR461647
- [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. Zbl0366.60057
- [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. Zbl0399.47039MR519680
- [38] A. Pietsch: Weyl numbers and eigenvalues of operators in Banach spaces, Math. Annalen (1980). Zbl0428.47027MR568205
- [39] C. Preston: Banach spaces arising from some integral inequalities, Indiana UniversityMath. Journal20 (1971) 997-1015. Zbl0228.46024MR282209
- [40] C. Preston: Continuity properties of some Gaussian processes, Annals of Math. Stat.43 (1972) 285-292. Zbl0268.60044MR307316
- [41] Séminaire L. Schwartz sur les applications radonifiantes 1969-70, Ecole Polytechnique, Paris. Zbl0195.13003
- [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. Zbl0324.46034MR461107
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.