On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series

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Abstract

In this paper, we compute the reproducing kernel Bm,αz,w for the generalized Fock space Fm,α2(ℂ). The usual Fock space is the case when m=2. We express the reproducing kernel in terms of a suitable hypergeometric series 1Fq. In particular, we show that there is a close connection between B4,αz,w and the error function. We also obtain the closed forms of Bm,αz,w when m=1,2/3,1/2. Finally, we also prove that Bm,α(z,z) ∼ eα|z|m|z|m-2 as |z| → ∞.

Original languageEnglish
Article number1365674
JournalJournal of Function Spaces
Volume2021
DOIs
Publication statusPublished - 2021

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