On Borel convergence of double sequences

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:68 Issue:2
On Borel convergence of double sequences

On Borel convergence of double sequences

Pages : 1289-1293

View : 42 | Download : 11

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :In this paper, we introduce the concept of insert ignore into journalissuearticles values(Ber);-convergence of bounded double sequences in the Fock space Finsert ignore into journalissuearticles values(C²);. We show that every insert ignore into journalissuearticles values(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}insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(k^{i}t^{j});/insert ignore into journalissuearticles values(i!j!););=x.
Keywords : Borel convergence, Berezin symbol, Pringsheim`s sense, double sequence, reproducing kernel

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