On Borel convergence of double sequences

Authors : Ulas YAMANCİ

Pages : 1289-1293

Doi:10.31801/cfsuasmas.425391

View : 11 | Download : 9

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