{"paper":{"title":"Construction, Extension and Coupling of Frames on Finite Dimensional Pontryagin Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"German Escobar, Kevin Esmeral, Osmin Ferrer","submitted_at":"2014-08-27T22:34:12Z","abstract_excerpt":"In this paper we extend to finite-dimensional Pontryagin spaces the methods used in \\cite{CasazzaLeon,Deguang} to build frames from an adjoint and positive operator. It is proved that any frame in finite dimensional Pontryagin space $\\mathcal{K}$ is $J$-orthogonal projection of a frame for a space $\\mathcal{H}$ such that $\\mathcal{K}\\subset\\mathcal{H}$. Furthermore, given $\\{k_{n}\\}_{n=1}^{m}$ and $\\{x_{n}\\}_{n=1}^{k}$ frames for $\\mathcal{K}$ and $\\mathcal{H}$ respectively, we build a finite-dimensional Pontryagin space $\\mathfrak{K}$ and a frame $\\{y_{n}\\}_{n=1}^{N}$ for $\\mathfrak{K}$ such "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6584","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"}