{"paper":{"title":"The Feichtinger conjecture for reproducing kernels in model subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Anton Baranov, Konstantin Dyakonov","submitted_at":"2009-06-11T16:57:09Z","abstract_excerpt":"We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace $K_\\Theta = H^2\\ominus \\Theta H^2$ of the Hardy space $H^2$, where $\\Theta$ is an inner function. First, we verify the Feichtinger conjecture for the kernels $ \\tilde k_{\\lambda_n} = k_{\\lambda_n}/\\|k_{\\lambda_n}\\|$ under the assumption that $\\sup_n |\\Theta(\\lambda_n)|<1$. Secondly, we prove the Feichtinger conjecture in the case where $\\Theta$ is a one-component inner function, meaning that the set $\\{z:|\\Theta(z)|<\\varepsilon\\}$ is connected for some $\\varepsilon\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2158","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"}