Geodesic flow and decay of traces on hyperbolic surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911768832376832 |
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| author | Gansemer, Antoine Hassell, Andrew |
| author_facet | Gansemer, Antoine Hassell, Andrew |
| contents | We study pseudodifferential operators on a hyperbolic surface using `Zelditch quantization'. We motivate and study the trace of $A_2^* A_1(t)$, where $A_2$ is a fixed operator and the Zelditch symbol of $A_1(t)$ evolves by geodesic flow. We find conditions under which the trace decays exponentially as $t \to \pm \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geodesic flow and decay of traces on hyperbolic surfaces Gansemer, Antoine Hassell, Andrew Spectral Theory Dynamical Systems 58J40 (Primary) 37D20, 11F72, 30Fxx (Secondary) We study pseudodifferential operators on a hyperbolic surface using `Zelditch quantization'. We motivate and study the trace of $A_2^* A_1(t)$, where $A_2$ is a fixed operator and the Zelditch symbol of $A_1(t)$ evolves by geodesic flow. We find conditions under which the trace decays exponentially as $t \to \pm \infty$. |
| title | Geodesic flow and decay of traces on hyperbolic surfaces |
| topic | Spectral Theory Dynamical Systems 58J40 (Primary) 37D20, 11F72, 30Fxx (Secondary) |
| url | https://arxiv.org/abs/2402.00230 |