Upper bound of the counting function of Steklov eigenvalues
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866909385968582656 |
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| author | He, Fei Wang, Lihan |
| author_facet | He, Fei Wang, Lihan |
| contents | We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be viewed as a weakened version of Pólya's Conjecture in the Steklov case on general manifolds. As a byproduct, we also obtain a description about the decay behavior of Steklov eigenfunctions near the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Upper bound of the counting function of Steklov eigenvalues He, Fei Wang, Lihan Spectral Theory Differential Geometry We study the counting function of Steklov eigenvalues on compact manifolds with boundary and obtain its upper bound involving the leading term of Weyl's law. Our estimate can be viewed as a weakened version of Pólya's Conjecture in the Steklov case on general manifolds. As a byproduct, we also obtain a description about the decay behavior of Steklov eigenfunctions near the boundary. |
| title | Upper bound of the counting function of Steklov eigenvalues |
| topic | Spectral Theory Differential Geometry |
| url | https://arxiv.org/abs/2411.07566 |