{"paper":{"title":"Multivariate Spectral Multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B{\\l}a\\.zej Wr\\'obel","submitted_at":"2014-07-09T09:05:03Z","abstract_excerpt":"This thesis is devoted to the study of multivariate (joint) spectral multipliers for systems of strongly commuting non-negative self-adjoint operators, $L=(L_1,\\ldots,L_d),$ on $L^2(X,\\nu),$ where $(X,\\nu)$ is a measure space. By strong commutativity we mean that the operators $L_r,$ $r=1,\\ldots,d,$ admit a joint spectral resolution $E(\\lambda).$ In that case, for a bounded function $m\\colon [0,\\infty)^d\\to \\mathbb{C},$ the multiplier operator $m(L)$ is defined on $L^2(X,\\nu)$ by\n  $$m(L)=\\int_{[0,\\infty)^d}m(\\lambda)dE(\\lambda).$$\n  By spectral theory, $m(L)$ is then bounded on $L^2(X,\\nu).$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2393","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"}