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Semigroup asymptotics, Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian

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posted on 2023-06-09, 13:08 authored by Stuart Day, Ali TaheriAli Taheri
A trace formulation of the Maclaurin spectral coefficients of the Schwartzian kernel of functions of the spherical Laplacian is given. A class of polynomials Pv/l (X) (l >_ 0, v > -1/2) linking to the classical Gegenbauer polynomials through a differential-spectral identity is introduced and its connection to the above spectral coefficients and their asymptotics analysed. The paper discusses some applications of these ideas combined with the Funk-Hecke identity and semigroup techniques to geometric and variational-energy inequalities on the sphere and presents some examples.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Rocky Mountain Journal of Mathematics

ISSN

0035-7596

Publisher

Rocky Mountain Mathematics Consortium

Issue

3

Volume

48

Page range

791-817

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-05-03

First Open Access (FOA) Date

2018-05-04

First Compliant Deposit (FCD) Date

2018-05-02

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