{"paper":{"title":"Spectral multipliers for functions of fixed $K$-type on $L^p(SL(2,\\mathbb{R}))$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SP"],"primary_cat":"math.FA","authors_text":"B{\\l}a\\.zej Wr\\'obel, Fulvio Ricci","submitted_at":"2018-09-25T09:51:53Z","abstract_excerpt":"We prove an $L^p$ spectral multiplier theorem for functions of the $K$-invariant sublaplacian $L$ acting on the space of functions of fixed $K$-type on the group $SL(2,\\mathbb{R}).$ As an application we compute the joint $L^p(SL(2,\\mathbb{R}))$ spectrum of $L$ and the derivative along $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09385","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"}