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

Day, Stuart and Taheri, Ali (2018) Semigroup asymptotics, Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian. Rocky Mountain Journal of Mathematics, 48 (3). pp. 791-817. ISSN 0035-7596

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 03 May 2018 10:56
Last Modified: 10 Aug 2018 08:04
URI: http://srodev.sussex.ac.uk/id/eprint/75591

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