Explicit formula for the reproducing kernels for some weighted Fock spaces

Cho, Hong Rae; Choi, Hyunil; Lee, Han-Wool

doi:10.1016/j.jmaa.2020.124920

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…But they did not obtain the explicit forms of the integral kernel. In [10], Cho et al computed the Fock kernel for the space with respect to dμ α ðzÞ = c α jzj 2α e −jzj 2 dV ðzÞ. For α > 0, the kernel K α ðz, wÞ is represented by K α ðz, wÞ= 1 F 1 ðn, n + α ; hz, wiÞ for z, w ∈ ℂ n .…”

Section: Introductionmentioning

confidence: 99%

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

Park

2021

Journal of Function Spaces

View full text Add to dashboard Cite

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 ∣ ⟶ ∞ .

show abstract

Section: Introductionmentioning

confidence: 99%