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arXiv · 2312.07078

A generalization of a result of Minakshisundaram and Pleijel

Ankita Sharma·Mansi Mishra·M. K. Vemuri
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Abstract

Minakshisundaram and Pleijel gave an asymptotic formula for the sum of squares of the pointwise values of the eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold, with eigenvalues less than a fixed number. Zelditch later extended this result by replacing the pointwise values with the Fourier coefficients of a smooth measure supported on a compact submanifold. Zelditch's result is very general, and his proof relies on the theory of Fourier integral operators. Here we give a proof based on methods of Riemannian geometry.

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Ankita Sharma, Mansi Mishra, M. K. Vemuri. 2023-12-12. A generalization of a result of Minakshisundaram and Pleijel. https://arxiv.org/abs/2312.07078

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