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

On donne une complète caractérisation de la suite des nombres (an) telle que n1anΦn converge, presque partout, pour tout système orthogonal (Φn) dans tout espace L2.

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

We characterize sequences of numbers (an) such that n1anΦn converges a.e. for any orthonormal system (Φn) in any L2-space.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.07.012

Adam Paszkiewicz 1

1 Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, PL-90-238 Łódź, Poland
@article{CRMATH_2009__347_19-20_1213_0,
     author = {Adam Paszkiewicz},
     title = {The explicit characterization of coefficients of a.e. convergent orthogonal series},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1213--1216},
     publisher = {Elsevier},
     volume = {347},
     number = {19-20},
     year = {2009},
     doi = {10.1016/j.crma.2009.07.012},
     language = {en},
}
TY  - JOUR
AU  - Adam Paszkiewicz
TI  - The explicit characterization of coefficients of a.e. convergent orthogonal series
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1213
EP  - 1216
VL  - 347
IS  - 19-20
PB  - Elsevier
DO  - 10.1016/j.crma.2009.07.012
LA  - en
ID  - CRMATH_2009__347_19-20_1213_0
ER  - 
%0 Journal Article
%A Adam Paszkiewicz
%T The explicit characterization of coefficients of a.e. convergent orthogonal series
%J Comptes Rendus. Mathématique
%D 2009
%P 1213-1216
%V 347
%N 19-20
%I Elsevier
%R 10.1016/j.crma.2009.07.012
%G en
%F CRMATH_2009__347_19-20_1213_0
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/

[1] V.F. Gaposhkin On convergence of orthogonal series, Dokl. Akad. Nauk SSSR, Volume 159 (1964), pp. 243-246 (in Russian)

[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

Cité par Sources :

Commentaires - Politique