{"paper":{"title":"Decomposition of the tensor product of two Hilbert modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gadadhar Misra, Soumitra Ghara","submitted_at":"2019-06-09T18:38:00Z","abstract_excerpt":"Given a pair of positive real numbers $\\alpha, \\beta$ and a sesqui-analytic function $K$ on a bounded domain $\\Omega \\subset \\mathbb C^m$, in this paper, we investigate the properties of the sesqui-analytic function $\\mathbb K^{(\\alpha, \\beta)}:= K^{\\alpha+\\beta}\\big(\\partial_i\\bar{\\partial}_j\\log K\\big )_{i,j=1}^ m,$ taking values in $m\\times m$ matrices. One of the key findings is that $\\mathbb K^{(\\alpha, \\beta)}$ is non-negative definite whenever $K^\\alpha$ and $K^\\beta$ are non-negative definite. In this case, a realization of the Hilbert module determined by the kernel $\\mathbb K^{(\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03687","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"}