{"paper":{"title":"Decay estimates for the one-dimensional wave equation with an inverse power potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Roland Donninger, Wilhelm Schlag","submitted_at":"2009-11-16T22:15:18Z","abstract_excerpt":"We study the wave equation on the real line with a potential that falls off like $|x|^{-\\alpha}$ for $|x| \\to \\infty$ where $2 < \\alpha \\leq 4$. We prove that the solution decays pointwise like $t^{-\\alpha}$ as $t \\to \\infty$ provided that there are no resonances at zero energy and no bound states. As an application we consider the $\\ell=0$ Price Law for Schwarzschild black holes. This paper is part of our investigations into decay of linear waves on a Schwarzschild background."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3174","kind":"arxiv","version":2},"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"}