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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@article{CRMATH_2013__351_5-6_177_0, author = {Karaev, Mubariz T.}, 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}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2013.02.016/} }
TY - JOUR AU - Karaev, Mubariz T. 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 UR - http://archive.numdam.org/articles/10.1016/j.crma.2013.02.016/ DO - 10.1016/j.crma.2013.02.016 LA - en ID - CRMATH_2013__351_5-6_177_0 ER -
%0 Journal Article %A Karaev, Mubariz T. %T Tauberian-type theorem for (e)-convergent sequences %J Comptes Rendus. Mathématique %D 2013 %P 177-179 %V 351 %N 5-6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2013.02.016/ %R 10.1016/j.crma.2013.02.016 %G en %F CRMATH_2013__351_5-6_177_0
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://archive.numdam.org/articles/10.1016/j.crma.2013.02.016/
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☆ Supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.