Comptes Rendus
no. 5-6
Complex Analysis/Functional Analysis
Tauberian-type theorem for (e)-convergent sequences

Présenté par : the Editorial Board

Mubariz T. Karaev1
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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.016
Mubariz T. Karaev 1

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

[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

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

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