{"paper":{"title":"Spectral synthesis in de Branges spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Alexander Borichev, Anton Baranov, Yurii Belov","submitted_at":"2013-09-26T14:24:55Z","abstract_excerpt":"We solve completely the spectral synthesis problem for reproducing kernels in the de Branges spaces $\\mathcal{H}(E)$. Namely, we describe the de Branges spaces $\\mathcal{H}(E)$ such that all $M$-bases of reproducing kernels (i.e., complete and minimal systems $\\{k_\\lambda\\}_{\\lambda\\in\\Lambda}$ with complete biorthogonal $\\{g_\\lambda\\}_{\\lambda\\in\\Lambda}$) are strong $M$-bases (i.e., every mixed system $\\{k_\\lambda\\}_{\\lambda\\in\\Lambda\\setminus\\tilde \\Lambda} \\cup\\{g_\\lambda\\}_{\\lambda\\in \\tilde \\Lambda}$ is also complete). Surprisingly this property takes place only for two essentially diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6915","kind":"arxiv","version":2},"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"}