Asymptotic Identities for Jacobi Polynomials via Spectral Geometry of Rank-One Symmetric Spaces

Ankita Sharma

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arXiv · 2504.20548

Asymptotic Identities for Jacobi Polynomials via Spectral Geometry of Rank-One Symmetric Spaces

Ankita Sharma

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Abstract

Radial eigenfunctions of the Laplace-Beltrami operator on compact rank-one symmetric spaces may be expressed in terms of Jacobi polynomials. We use this fact to prove an identity for Jacobi polynomials which is inspired by results of Minakshisundaram-Pleijel and Zelditch on the Fourier coefficients of a smooth measure supported on a compact submanifold of a compact Riemannian manifold.

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BibTeX RIS

Ankita Sharma. 2025-04-29. Asymptotic Identities for Jacobi Polynomials via Spectral Geometry of Rank-One Symmetric Spaces. https://arxiv.org/abs/2504.20548

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