A generalization of a result of Minakshisundaram and Pleijel
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909457275944960 |
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| author | Sharma, Ankita Mishra, Mansi Vemuri, M. K. |
| author_facet | Sharma, Ankita Mishra, Mansi Vemuri, M. K. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_07078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A generalization of a result of Minakshisundaram and Pleijel Sharma, Ankita Mishra, Mansi Vemuri, M. K. Differential Geometry Spectral Theory 53B21, 58J35 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. |
| title | A generalization of a result of Minakshisundaram and Pleijel |
| topic | Differential Geometry Spectral Theory 53B21, 58J35 |
| url | https://arxiv.org/abs/2312.07078 |