Complex Analysis/Functional Analysis
Tauberian-type theorem for (e)-convergent sequences
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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.02.016
Karaev, Mubariz T. 1

1 Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Karaev, Mubariz T. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.02.016/

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

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

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

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

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

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

[7] Powell, R.E.; Shah, S.M. 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.