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ON ABEL CONVERGENCE OF DOUBLE SEQUENCES
Journal article   Peer reviewed

ON ABEL CONVERGENCE OF DOUBLE SEQUENCES

M. T. Karaev and M. Zeltser
Numerical functional analysis and optimization, Vol.31(10), pp.1185-1189
10/2010
DOI: https://doi.org/10.1080/01630563.2010.501263

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
In terms of Berezin symbols, we give the concept of (Ber)-convergence of bounded double sequences. We prove that every (Ber)-convergent double sequence is Abel convergent. In particular, by using the Berezin symbols technique, we prove the following double sequence analog of the classical Abel theorem for the sequences: If the sequence {a(mn) }(infinity)(m,n=0) regularly converges to L, then lim(x -> 1)(,y -> 1)(-)(-) (1-x) (1-y) Sigma(infinity)(m-0) Sigma(infinity)(n-0) a(mn)x(m)y(m) = L.

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