The Birman-Krein Trace Formula and Scattering Phase on Product space
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909775639347200 |
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| author | Zhang, Hong |
| author_facet | Zhang, Hong |
| contents | In this paper, we study the Birman-Krein formula for the potential scattering on the product space $\mathbb{R}^n\times M$, where $M$ is a compact Riemannian manifold possibly with boundary, and $\mathbb{R}^N$ is the Euclidean space with $n\geq 3$ being an odd number. We also derive an upper bound for the scattering trace when $M$ is a bounded Euclidean domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Birman-Krein Trace Formula and Scattering Phase on Product space Zhang, Hong Spectral Theory In this paper, we study the Birman-Krein formula for the potential scattering on the product space $\mathbb{R}^n\times M$, where $M$ is a compact Riemannian manifold possibly with boundary, and $\mathbb{R}^N$ is the Euclidean space with $n\geq 3$ being an odd number. We also derive an upper bound for the scattering trace when $M$ is a bounded Euclidean domain. |
| title | The Birman-Krein Trace Formula and Scattering Phase on Product space |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2509.06372 |