{"paper":{"title":"Spectral properties of Schr\\\"{o}dinger-type operators and large-time behavior of the solutions to the corresponding wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"A. G. Ramm","submitted_at":"2012-06-26T13:57:48Z","abstract_excerpt":"Let $L$ be a linear, closed, densely defined in a Hilbert space operator, not necessarily selfadjoint.\n  Consider the corresponding wave equations\n  &(1) \\quad \\ddot{w}+ Lw=0, \\quad w(0)=0,\\quad \\dot{w}(0)=f, \\quad \\dot{w}=\\frac{dw}{dt}, \\quad f \\in H.\n  &(2) \\quad \\ddot{u}+Lu=f e^{-ikt}, \\quad u(0)=0, \\quad \\dot{u}(0)=0,\nwhere $k>0$ is a constant. Necessary and sufficient conditions are given for the operator $L$ not to have eigenvalues in the half-plane Re$z<0$ and not to have a positive eigenvalue at a given point $k_d^2 >0$. These conditions are given in terms of the large-time behavior of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5990","kind":"arxiv","version":1},"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"}