{"paper":{"title":"Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luchezar Stoyanov, Vesselin Petkov","submitted_at":"2009-06-01T14:23:31Z","abstract_excerpt":"Let $s_0 < 0$ be the abscissa of absolute convergence of the dynamical zeta function $Z(s)$ for several disjoint strictly convex compact obstacles $K_i \\subset \\R^N, i = 1,..., \\kappa_0,\\: \\ka_0 \\geq 3,$ 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 $\\Omega = \\bar{\\R^N \\setminus \\cup_{i = 1}^{k_0} K_i}$. 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) < "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0293","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}