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2018 Semigroup asymptotics, the Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian
Stuart Day, Ali Taheri
Rocky Mountain J. Math. 48(3): 791-817 (2018). DOI: 10.1216/RMJ-2018-48-3-791

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 $\mathscr {P}^\nu _l(X)$ $(l \ge 0$, $\nu \gt -1/2)$ linking to the classical Gegenbauer polynomials through a differential-spectral identity is introduced, and its connection to the above spectral coefficients and their asymptotics analyzed. 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.

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Stuart Day. Ali Taheri. "Semigroup asymptotics, the Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian." Rocky Mountain J. Math. 48 (3) 791 - 817, 2018. https://doi.org/10.1216/RMJ-2018-48-3-791

Information

Published: 2018
First available in Project Euclid: 2 August 2018

zbMATH: 06917347
MathSciNet: MR3835572
Digital Object Identifier: 10.1216/RMJ-2018-48-3-791

Subjects:
Primary: 47B25, 47F05
Secondary: 33C05, 33C20, 33C45, 47D06, 47E05, 58J35

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 3 • 2018
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