{"paper":{"title":"The Malgrange-Ehrenpreis theorem for nonlocal Schr\\\"odinger operators with certain potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Woocheol Choi, Yong-Cheol Kim","submitted_at":"2016-12-15T11:05:21Z","abstract_excerpt":"In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schr\\\"odinger operators $L_K+V$ with nonnegative potentials $V\\in L^q_{\\loc}(\\BR^n)$ for $q>\\f{n}{2s}$ with $0<s<1$ and $n\\ge 2$; that is to say, we obtain the existence of a fundamental solution $\\fe_V$ for $L_K+V$ satisfying \\begin{equation*}\\bigl(L_K+V\\bigr)\\fe_V=\\dt_0\\,\\,\\text{ in $\\BR^n$ }\\end{equation*} in the distribution sense, where $\\dt_0$ denotes the Dirac delta mass at the origin. In addition, we obtain a decay of the fundamental solution $\\fe_V$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07143","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"}