Tauberian-type theorem for (<i>e</i>)-convergent sequences

Mubariz T. Karaev

doi:10.1016/j.crma.2013.02.016

Complex Analysis/Functional Analysis

Tauberian-type theorem for (e)-convergent sequences

Presented by: the Editorial Board

Mubariz T. Karaev ¹

¹ Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 177-179.

Abstract

We prove a Tauberian-type theorem for (e)-convergent sequences, which were introduced by the author in Karaev (2010) [4]. Our proof is based on the Berezin symbols technique of operator theory in the reproducing kernel Hilbert space.

Received: 2013-01-23
Accepted: 2013-02-28
Published online: 2013-03-01

DOI: 10.1016/j.crma.2013.02.016

Author's affiliations:

Mubariz T. Karaev ¹

¹ Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

@article{CRMATH_2013__351_5-6_177_0,
     author = {Mubariz T. Karaev},
     title = {Tauberian-type theorem for (\protect\emph{e})-convergent sequences},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {177--179},
     publisher = {Elsevier},
     volume = {351},
     number = {5-6},
     year = {2013},
     doi = {10.1016/j.crma.2013.02.016},
     language = {en},
}

TY  - JOUR
AU  - Mubariz T. Karaev
TI  - Tauberian-type theorem for (e)-convergent sequences
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 177
EP  - 179
VL  - 351
IS  - 5-6
PB  - Elsevier
DO  - 10.1016/j.crma.2013.02.016
LA  - en
ID  - CRMATH_2013__351_5-6_177_0
ER  -

%0 Journal Article
%A Mubariz T. Karaev
%T Tauberian-type theorem for (e)-convergent sequences
%J Comptes Rendus. Mathématique
%D 2013
%P 177-179
%V 351
%N 5-6
%I Elsevier
%R 10.1016/j.crma.2013.02.016
%G en
%F CRMATH_2013__351_5-6_177_0

Mubariz T. Karaev. Tauberian-type theorem for (e)-convergent sequences. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 177-179. doi : 10.1016/j.crma.2013.02.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.016/

References
Cited by

[1] F.A. Berezin Covariant and contravariant symbols for operators, Math. USSR-Izv., Volume 6 (1972), pp. 1117-1151

[2] F.A. Berezin Quantization, Math. USSR-Izv., Volume 8 (1974), pp. 1109-1163

[3] G.H. Hardy Divergent Series, Clarendon Press, Oxford, 1956

[4] M.T. Karaev (e)-Convergence and related problem, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 1059-1062

[5] E. Nordgren; P. Rosenthal Boundary values of Berezin symbols, Oper. Theory Adv. Appl., Volume 73 (1994), pp. 362-368

[6] A.G. Postnikov Tauberian Theory and Its Applications, Proc. Steklov Inst. Math., vol. 144, Amer. Math. Soc., 1980

[7] R.E. Powell; S.M. Shah Summability Theory and Applications, Prentice-Hall, 1988

Cited by Sources:

^☆ Supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.

Comments - Policy