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Quaestiones Mathematicae

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Berezin symbols and Borel summability

M.T. Garayev, M Gürdal

Abstract


We prove in terms of so-called Berezin symbols some theorems for Borel summability method for sequences and series of complex numbers. Namely, we characterize the Borel convergent sequences and series; prove regularity of Borel summability method, and prove a new Tauberian type theorem for Borel summability.

Keywords: Borel summabiliy, Berezin symbol, diagonal operator, compact operator, (e)-convergence, Tauberian type theorem, Fock space




http://dx.doi.org/10.2989/16073606.2017.1289989
AJOL African Journals Online