A spectral identity on Jacobi polynomials and its analytic implications

Awonusika, Richard Olu and Taheri, Ali (2018) A spectral identity on Jacobi polynomials and its analytic implications. Canadian Mathematical Bulletin, 61. pp. 473-482. ISSN 0008-4395

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Abstract

The Jacobi coefficients c`j (; ) (1 j `, ; > 1) are linked to the Maclaurin spectral expansion of the Schwartz kernel of functions of the Laplacian on a compact rank one symmetric space. It is proved that these coefficients can be computed by transforming the even derivatives of the jacobi polynomials P(;) k (k 0; ; > 1) into a spectral sum associated with the Jacobi operator. The first few coefficients are explicitly computed and a direct trace interpretation of the Maclaurin coefficients is presented.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 06 Nov 2017 11:02
Last Modified: 10 Aug 2018 09:40
URI: http://sro.sussex.ac.uk/id/eprint/70937

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