{"paper":{"title":"On de Branges--Rovnyak Kernels Admitting a Complete Pick Factor","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Haripada Sau","submitted_at":"2026-06-08T16:00:28Z","abstract_excerpt":"For a contractive multiplier $\\varphi$ in the multiplier algebra $M(k)$ of a kernel $k$, the associated de Branges--Rovnyak kernel is given by $k^\\varphi(x,y) = (1-\\varphi(x)\\overline{\\varphi(y)})k(x,y)$. Motivated by recent developments clarifying the structural and geometric features of reproducing kernel Hilbert spaces associated with kernels admitting a complete Pick factor, we investigate the precise conditions for a general de Branges-Rovnyak kernel to admit a complete Pick factor, thereby extending the framework introduced by Ahmed, Das and Panja (\\textit{J. Geom. Anal.}, 2025). In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09680","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.09680/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}