{"paper":{"title":"On the Structure and Interpolation Properties of Quasi Shift-invariant Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Jeff Ledford, Keaton Hamm","submitted_at":"2017-03-04T22:58:03Z","abstract_excerpt":"The structure of certain types of quasi shift-invariant spaces, which take the form $V(\\psi,\\mathcal{X}):=\\overline{\\text{span}}^{L_2}\\{\\psi(\\cdot-x_j):j\\in\\mathbb{Z}\\}$ for a discrete set $\\mathcal{X}=(x_j)\\subset\\mathbb{R}$ is investigated. Additionally, the relation is explored between pairs $(\\psi,\\mathcal{X})$ and $(\\phi,\\mathcal{Y})$ such that interpolation of functions in $V(\\psi,\\mathcal{X})$ via interpolants in $V(\\phi,\\mathcal{Y})$ solely from the samples of the original function is possible and stable. Some conditions are given for which the sampling problem is stable, and for which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01533","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"}