{"paper":{"title":"The regularity of the $\\eta$ function for the Shubin calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Pedro Lopes","submitted_at":"2012-09-06T07:39:28Z","abstract_excerpt":"We prove the regularity of the $\\eta$ function for classical pseudodifferential operators with Shubin symbols. We recall the construction of complex powers and of the Wodzicki and Kontsevich-Vishik functionals for classical symbols on $\\mathbb{R}^{n}$ with these symbols. We then define the $\\zeta$ and $\\eta$ functions associated to suitable elliptic operators. We compute the $K_{0}$ group of the algebra of zero-order operators and use this knowledge to show that the Wodzicki trace of the idempotents in the algebra vanishes. From this, it follows that the $\\eta$ function is regular at 0 for any"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1206","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"}