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A spectral identity on Jacobi polynomials and its analytic implications
journal contribution
posted on 2023-06-09, 08:38 authored by Richard Olu Awonusika, Ali TaheriAli TaheriThe 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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Canadian Mathematical BulletinISSN
0008-4395Publisher
Canadian Mathematical SocietyExternal DOI
Volume
61Page range
473-482Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes