{"paper":{"title":"Homogeneous operators on Hilbert spaces of holomorphic functions -- I","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.FA","authors_text":"Adam Kor\\'anyi, Gadadhar Misra","submitted_at":"2006-09-06T04:48:35Z","abstract_excerpt":"In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are {\\em homogeneous} with respect to the action of the M\\\"{o}bius group consisting of bi-holomorphic automorphisms of the unit disc $\\mathbb D$. For every $m \\in \\N$ we have a family of operators depending on $m+1$ positive real parameters. The kernel function is calculated explicitly. It is proved that each of these operators is bounded, lies in the Cowen-Douglas class of $\\mathbb D$ and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609164","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"}