The explicit characterization of coefficients of a.e. convergent orthogonal series

Adam Paszkiewicz

doi:10.1016/j.crma.2009.07.012

Probability Theory/Mathematical Analysis

The explicit characterization of coefficients of a.e. convergent orthogonal series
[Caractérisation explicite des coefficients des séries orthogonales convergentes presques partout]

Présenté par : Michel Talagrand

Adam Paszkiewicz ¹

¹ Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, PL-90-238 Łódź, Poland

Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1213-1216.

Abstract (VO)
Résumé

We characterize sequences of numbers $(a_{n})$ such that $\sum_{n ⩾ 1} a_{n} Φ_{n}$ converges a.e. for any orthonormal system $(Φ_{n})$ in any $L_{2}$ -space.

On donne une complète caractérisation de la suite des nombres $(a_{n})$ telle que $\sum_{n ⩾ 1} a_{n} Φ_{n}$ converge, presque partout, pour tout système orthogonal $(Φ_{n})$ dans tout espace $L_{2}$ .

La démonstration détaillées est donnée par A. Paszkiewicz dans l'article : On complete characterization of coefficients of a.e. convergent orthogonal series.

Reçu le : 2008-03-16
Accepté le : 2009-07-15
Publié le : 2009-09-15

DOI : 10.1016/j.crma.2009.07.012

Affiliations des auteurs :

Adam Paszkiewicz ¹

¹ Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, PL-90-238 Łódź, Poland

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Adam Paszkiewicz. The explicit characterization of coefficients of a.e. convergent orthogonal series. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1213-1216. doi : 10.1016/j.crma.2009.07.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.012/

Bibliographie
Cité par

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[2] A. Paszkiewicz, On complete characterization of coefficients of a.e. convergent orthogonal series and on majorizing measures, Invent. Math., in press

[3] M. Talagrand Sample boundedness of stochastic processes under increment conditions, Ann. Probab., Volume 18 (1990), pp. 1-49

[4] M. Talagrand, Convergence of orthogonal series using stochastic processes, unpublished manuscript

[5] K. Tandori Über die Konvergenz der Orthogonalreihen, Acta Sci. Math. (Szeged), Volume 24 (1963), pp. 139-151

[6] M. Weber Some theorems related to almost sure convergence of orthogonal series, Indag. Math. (N.S.), Volume 11 (2000), pp. 293-311

Safari Mukeru Some applications of the Menshov-Rademacher theorem, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 359 (2021) no. 7, pp. 861-870 | DOI:10.5802/crmath.225 | Zbl:1473.42006
Witold Bednorz The complete characterization of a.s. convergence of orthogonal series, The Annals of Probability, Volume 41 (2013) no. 2, pp. 1055-1071 | DOI:10.1214/11-aop712 | Zbl:1329.60062
Witold Bednorz On the convergence of orthogonal series, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 349 (2011) no. 7-8, pp. 455-458 | DOI:10.1016/j.crma.2011.02.001 | Zbl:1216.60023
Witold Bednorz Majorizing measures on metric spaces, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 348 (2010) no. 1-2, pp. 75-78 | DOI:10.1016/j.crma.2009.11.017 | Zbl:1185.60035

Cité par 4 documents. Sources : zbMATH

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