{"paper":{"title":"Pick matricies and quaternionic power series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Bolotnikov","submitted_at":"2014-05-14T22:03:12Z","abstract_excerpt":"It is well known that a non-constant complex-valued function $f$ defined on the open unit disk $\\mathbb D$ is an analytic self-mapping of $\\D$ if and only if Pick matrices $\\left[ (1-f(z_i)\\overline{f(z_j)})/(1-z_i\\overline{z}_j)\\right]_{i,j=1}^n$ are positive semidefinite for all choices of finitely many points $z_i\\in\\D$. A stronger version of the \"if\" part was established by Alan Hindmarsh: if all $3\\times 3$ Pick matrices are positive semidefinite, then $f$ is an analytic self-mapping of $\\mathbb D$. In this paper, we extend this result to the non-commutative setting of power series over q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3706","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"}