{"paper":{"title":"Radial Solutions of Non-Archimedean Pseudo-Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"math.CA","authors_text":"Anatoly N. Kochubei","submitted_at":"2013-02-20T09:45:01Z","abstract_excerpt":"We consider a class of equations with the fractional differentiation operator $D^\\alpha$, $\\alpha >0$, for complex-valued functions $x\\mapsto f(|x|_K)$ on a non-Archimedean local field $K$ depending only on the absolute value $|\\cdot |_K$. We introduce a right inverse $I^\\alpha$ to $D^\\alpha$, such that the change of an unknown function $u=I^\\alpha v$ reduces the Cauchy problem for an equation with $D^\\alpha$ (for radial functions) to an integral equation whose properties resemble those of classical Volterra equations. This contrasts much more complicated behavior of $D^\\alpha$ on other classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4850","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"}