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Geometric analysis proves new asymptotic identities for Jacobi polynomials on compact rank-one symmetric spaces, highlighting connections between spectral theory and special functions.
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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Ankita Sharma (2026) studied this question.
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