{"paper":{"title":"Geometry of reproducing kernels in model spaces near the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andreas Hartmann (IMB), Anton Baranov (SPSU), Karim Kellay (IMB)","submitted_at":"2015-09-30T08:46:25Z","abstract_excerpt":"We study two geometric properties of reproducing kernels in model spaces $K\\_\\theta$where $\\theta$ is an inner function in the disc: overcompleteness and existence of uniformly minimalsystems of reproducing kernels which do not contain Riesz basic sequences. Both of these properties are related to the notion of the Ahern--Clark point. It is shown that \"uniformly minimal non-Riesz\"$ $ sequences of reproducing kernelsexist near each Ahern--Clark point which is not an analyticity point for $\\theta$, whileovercompleteness may occur only near the Ahern--Clark points of infinite orderand is equivale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09077","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"}