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Operators of Laplace transform type and a new class of hypergeometric coefficients

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posted on 2023-06-09, 14:27 authored by Stuart Bond, Ali TaheriAli Taheri
A differential identity on the hypergeometric function ${}_2F_1(a,b;c;z)$ unifying and extending certain spectral results on the scale of Gegenbauer and Jacobi polynomials and leading to a new class of hypergeometric related scalars $\mathsf{c}_j^m(a,b,c)$ and polynomials $\mathscr{R}_m=\mathscr{R}_m(X)$ is established. The Laplace-Beltrami operator on a compact rank one symmetric space is considered next and for operators of the Laplace transform type by invoking an operator trace relation, the Maclaurin spectral coefficients of their Schwartz kernel are fully described. Other representations as well as extensions of the differential identity to the generalised hypergeometric function ${}_pF_q({\bf a}; {\bf b}; z)$ are formulated and proved.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Advances in Operator Theory

ISSN

2538-225X

Publisher

Tusi Mathematical Research Group

Issue

1

Volume

4

Page range

226-250

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-08-09

First Open Access (FOA) Date

2018-10-30

First Compliant Deposit (FCD) Date

2018-08-08

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