- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 2
- On Borel convergence of double sequences
On Borel convergence of double sequences
Authors : Ulas Yamanci
Pages : 1289-1293
Doi:10.31801/cfsuasmas.425391
View : 9 | Download : 4
Publication Date : 2019-08-01
Article Type : Research
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