On the Fock Kernel for the Generalized Fock Space and Generalized Hypergeometric Series. (23rd August 2021) - Park, Jong-Do
Abstract : In this paper, we compute the reproducing kernel B m, α z, w for the generalized Fock space F m, α 2 ℂ . The usual Fock space is the case when m = 2 . We express the reproducing kernel in terms of a suitable hypergeometric series   1 F q . In particular, we show that there is a close connection between B 4, α z, w and the error function. We also obtain the closed forms of B m, α z, w when m = 1, 2 / 3, 1 / 2 . Finally, we also prove that B m, α z, z ~ e α z m z m − 2 as ∣ z ∣ ⟶ ∞ .