On Borel convergence of double sequences

Year 2019, Volume: 68 Issue: 2, 1289 - 1293, 01.08.2019

Ulas Yamanci

https://doi.org/10.31801/cfsuasmas.425391

Cited By: 1

Abstract

In this paper, we introduce the concept of (Ber)-convergence of bounded double sequences in the Fock space F(C²). We show that every (Ber)-convergent double sequence is Borel convergent. Namely, we prove the following theorem by using the Berezin symbol method: If the {x_{ij}}_{i,j=0}^{∞} is regularly convergent to x, then

lim_{k,l→∞}e^{-k-l}∑_{i,j=0}^{∞}x_{ij}((k^{i}t^{j})/(i!j!))=x.

Keywords

Borel convergence, Berezin symbol, Pringsheim's sense, double sequence, reproducing kernel

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