From quasimodes to resonances: exponentially decaying perturbations
| Autor: | Oran Gannot |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
General Mathematics
media_common.quotation_subject Mathematical analysis Multiplicity (mathematics) Mathematics::Spectral Theory Type (model theory) Infinity Exponential function Mathematics - Spectral Theory Mathematics - Analysis of PDEs Maximum principle FOS: Mathematics Spectral Theory (math.SP) Laplace operator Analysis of PDEs (math.AP) Resolvent media_common Mathematics Meromorphic function |
| Zdroj: | Pacific Journal of Mathematics. 277:77-97 |
| ISSN: | 0030-8730 |
| DOI: | 10.2140/pjm.2015.277.77 |
| Popis: | We consider self-adjoint operators of black-box type which are exponentially close to the free Laplacian near infinity, and prove an exponential bound for the resolvent in a strip away from resonances. Here the resonances are defined as poles of the meromorphic continuation of the resolvent between appropriate exponentially weighted spaces. We then use a local version of the maximum principle to prove that any cluster of real quasimodes generates at least as many resonances, with multiplicity, rapidly converging to the quasimodes. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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