On Borel convergence of double sequences
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.