{"paper":{"title":"On regularization of Mellin PDO's with slowly oscillating symbols of limited smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Amarino B. Lebre, Yuri I. Karlovich","submitted_at":"2014-07-12T18:52:45Z","abstract_excerpt":"We study Mellin pseudodifferential operators (shortly, Mellin PDO's) with symbols in the algebra $\\widetilde{\\mathcal{E}}(\\mathbb{R}_+,V(\\mathbb{R}))$ of slowly oscillating functions of limited smoothness introduced in \\cite{K09}. We show that if $\\mathfrak{a}\\in\\widetilde{\\mathcal{E}}(\\mathbb{R}_+,V(\\mathbb{R}))$ does not degenerate on the \"boundary\" of $\\mathbb{R}_+\\times\\mathbb{R}$ in a certain sense, then the Mellin PDO ${\\rm Op}(\\mathfrak{a})$ is Fredholm on the space $L^p$ for $p\\in(1,\\infty)$ and each its regularizer is of the form ${\\rm Op}(\\mathfrak{b})+K$ where $K$ is a compact opera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3411","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"}