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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16652 |
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| _version_ | 1866929644262916096 |
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| author | Pérez-Esteva, S. Uribe, A. Villegas-Blas, C. |
| author_facet | Pérez-Esteva, S. Uribe, A. Villegas-Blas, C. |
| contents | We study the spectrum of the Dirichlet to Neumann operator of the two-sphere associated to a Schrödinger operator in the unit ball. The spectrum forms clusters of size $O(1/k)$ around the sequence of natural numbers $k=1,2,\ldots$, and we compute the first three terms in the asymptotic distribution of the eigenvalues within the clusters, as $k\to\infty$ (band invariants). There are two independent aspects of the proof. The first is a study of the Berezin symbol of the Dirichlet to Neumann operator, which arises after one applies the averaging method. The second is the use of a symbolic calculus of Berezin-Toeplitz operators on the manifold of closed geodesics of the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral cluster asymptotics of the Dirichlet to Neumann operator on the two-sphere Pérez-Esteva, S. Uribe, A. Villegas-Blas, C. Spectral Theory We study the spectrum of the Dirichlet to Neumann operator of the two-sphere associated to a Schrödinger operator in the unit ball. The spectrum forms clusters of size $O(1/k)$ around the sequence of natural numbers $k=1,2,\ldots$, and we compute the first three terms in the asymptotic distribution of the eigenvalues within the clusters, as $k\to\infty$ (band invariants). There are two independent aspects of the proof. The first is a study of the Berezin symbol of the Dirichlet to Neumann operator, which arises after one applies the averaging method. The second is the use of a symbolic calculus of Berezin-Toeplitz operators on the manifold of closed geodesics of the sphere. |
| title | Spectral cluster asymptotics of the Dirichlet to Neumann operator on the two-sphere |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2412.16652 |