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Winter 2019 Operators of Laplace transform type and a new class of hypergeometric coefficients
Stuart Bond, Ali Taheri
Adv. Oper. Theory 4(1): 226-250 (Winter 2019). DOI: 10.15352/aot.1804-1356

Abstract

‎‎‎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 related representations as well as extensions of the differential‎ ‎identity to the generalized hypergeometric function ${}_pF_q(\textbf{a}; \textbf{b}; z)$ are formulated and proved‎.

Citation

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Stuart Bond. Ali Taheri. "Operators of Laplace transform type and a new class of hypergeometric coefficients." Adv. Oper. Theory 4 (1) 226 - 250, Winter 2019. https://doi.org/10.15352/aot.1804-1356

Information

Received: 30 April 2018; Accepted: 15 July 2018; Published: Winter 2019
First available in Project Euclid: 27 July 2018

zbMATH: 06946452
MathSciNet: MR3867343
Digital Object Identifier: 10.15352/aot.1804-1356

Subjects:
Primary: 47F05

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 1 • Winter 2019
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