{"paper":{"title":"On some spectral properties of pseudo-differential operators on T","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Juan Pablo Velasquez-Rodriguez","submitted_at":"2019-01-31T21:00:20Z","abstract_excerpt":"In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\\mathbb{T} := \\mathbb{R}/ 2 \\pi \\mathbb{ Z}$. For symbols in the H\\\"ormander class $S^m_{1 , 0} (\\mathbb{T} \\times \\mathbb{Z})$, we provide a sufficient and necessary condition to ensure that the corresponding pseudo-differential operator is a Riesz operator in $L^p (\\mathbb{T})$, $1< p < \\infty$, extending in this way compact operators characterisation and Ghoberg's lemma to $L^p (\\mathbb{T})$. We provide an exampl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00070","kind":"arxiv","version":4},"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"}