{"paper":{"title":"Fourier multipliers, symbols and nuclearity on compact manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.FA","authors_text":"Julio Delgado, Michael Ruzhansky","submitted_at":"2014-04-25T16:49:46Z","abstract_excerpt":"The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence, given a compact manifold endowed with a positive measure, we introduce a notion of the operator's full symbol adapted to the Fourier analysis relative to a fixed elliptic operator. We give a description of Fourier multipliers, or of operators invariant relative to the elliptic operator. We apply these concepts to study Schatten classes of operators and to obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6479","kind":"arxiv","version":2},"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"}