{"paper":{"title":"Non-Archimedean Pseudo-Differential Operators With Bessel Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"Anselmo Torresblanca-Badillo, Ismael Guti\\'errez Garc\\'ia","submitted_at":"2019-04-01T23:33:50Z","abstract_excerpt":"In this article, we study a class of non-archimedean pseudo-differential operators associated via Fourier transform to the Bessel potentials. These operators (which we will denote as $J^{\\alpha },$ $\\alpha >n$) are of the form (J^{\\alpha })(x)=\\mathcal{F}_{\\xi \\rightarrow x}^{-1}\\left[ (\\max\\{1,||\\xi ||_{p}\\})^{-\\alpha }\\widehat{\\varphi }(\\xi )\\right] ,\\text{ } \\varphi \\in \\mathcal{D}\\mathbb{Q}_{p}^{n}),\\text{ } x\\in\\mathbb{Q}_{p}^{n}. We show that the fundamental solution $Z(x,t)$ of the $p-$adic heat equation naturally associated to these operators satisfies $Z(x,t)<= 0,x\\in\\mathbb{Q} _{p}^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01968","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"}