On some spectral properties of the weighted \(\overline\partial\)-Neumann problem
We derive a necessary condition for compactness of the weighted \(\overline\partial\)-Neumann operator on the space \(L^2(\mathbb C^n,e^{-\varphi})\), under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension. Moreover, we compute the essential spe...
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| Vydané v: | arXiv.org |
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| Hlavní autori: | , |
| Médium: | Paper |
| Jazyk: | English |
| Vydavateľské údaje: |
Ithaca
Cornell University Library, arXiv.org
12.10.2016
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| Predmet: | |
| ISSN: | 2331-8422 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | We derive a necessary condition for compactness of the weighted \(\overline\partial\)-Neumann operator on the space \(L^2(\mathbb C^n,e^{-\varphi})\), under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension. Moreover, we compute the essential spectrum of the complex Laplacian for decoupled weights, \(\varphi(z) = \varphi_1(z_1) + \dotsb + \varphi_n(z_n)\), and investigate (non-) compactness of the \(\overline\partial\)-Neumann operator in this case. More can be said if every \(\Delta\varphi_j\) defines a nontrivial doubling measure. |
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| Bibliografia: | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| ISSN: | 2331-8422 |
| DOI: | 10.48550/arxiv.1509.08741 |