{"paper":{"title":"Location of maximizers of eigenfunctions of fractional Schr\\\"odinger's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.AP","authors_text":"Anup Biswas","submitted_at":"2017-07-26T11:50:42Z","abstract_excerpt":"Eigenfunctions of the fractional Schr\\\"odinger operators in a domain $\\mathcal{D}$ are considered, and a relation between the supremum of the potential and the distance of a maximizer of the eigenfunction from $\\partial\\mathcal{D}$ is established. This, in particular, extends a recent result of Rachh and Steinerberger to the fractional Schr\\\"odinger operators. We also propose a fractional version of the Barta's inequality and also generalize a celebrated Lieb's theorem for fractional Schr\\\"odinger operators. As applications of above results we obtain a Faber-Krahn inequality for non-local Schr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08392","kind":"arxiv","version":3},"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"}