Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| hal.structure.identifier | School of Mathematics and Statistics [Crawley, Perth] | |
| dc.contributor.author | STOYANOV, Luchezar | |
| dc.date.accessioned | 2024-04-04T02:36:52Z | |
| dc.date.available | 2024-04-04T02:36:52Z | |
| dc.date.created | 2008 | |
| dc.date.issued | 2010 | |
| dc.identifier.issn | 2157-5045 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190756 | |
| dc.description.abstractEn | Let $s_0 < 0$ be the abscissa of absolute convergence of the dynamical zeta function $Z(s)$ for several disjoint strictly convex compact obstacles $K_i \subset \R^N, i = 1,\ldots, \kappa_0,\: \ka_0 \geq 3,$ and let $R_{\chi}(z) = \chi (-\Delta_D - z^2)^{-1}\chi,\: \chi \in C_0^{\infty}(\R^N),$ be the cut-off resolvent of the Dirichlet Laplacian $-\Delta_D$ in $\Omega = \overline{\R^N \setminus \cup_{i = 1}^{k_0} K_i}$. We prove that there exists $\sigma_1 < s_0$ such that $Z(s)$ is analytic for $\Re (s) \geq \sigma_1$ and the cut-off resolvent $R_{\chi}(z)$ has an analytic continuation for $\Im (z) < - \sigma_1,\: |\Re (z)| \geq C > 0.$ | |
| dc.language.iso | en | |
| dc.publisher | Mathematical Sciences Publishers | |
| dc.title.en | Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.2140/apde.2010.3.427 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 0906.0293 | |
| bordeaux.journal | Analysis & PDE | |
| bordeaux.page | 427-489 | |
| bordeaux.volume | 3 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00391722 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00391722v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Analysis%20&%20PDE&rft.date=2010&rft.volume=3&rft.issue=4&rft.spage=427-489&rft.epage=427-489&rft.eissn=2157-5045&rft.issn=2157-5045&rft.au=PETKOV,%20Vesselin&STOYANOV,%20Luchezar&rft.genre=article |
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