AOT-Hypergeometric_TMRG_11_07_2018.pdf (364.27 kB)
Operators of Laplace transform type and a new class of hypergeometric coefficients
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 TheoryISSN
2538-225XPublisher
Tusi Mathematical Research GroupExternal DOI
Issue
1Volume
4Page range
226-250Department 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
2018-08-09First Open Access (FOA) Date
2018-10-30First Compliant Deposit (FCD) Date
2018-08-08Usage metrics
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