{"paper":{"title":"Construction of frames for shift-invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stevan Pilipovic, Suzana Simic","submitted_at":"2011-09-15T08:17:23Z","abstract_excerpt":"We construct a sequence ${\\phi_i(\\cdot-j)\\mid j\\in{\\ZZ}, i=1,...,r}$ which constitutes a $p$-frame for the weighted shift-invariant space [V^p_{\\mu}(\\Phi)=\\Big{\\sum\\limits_{i=1}^r\\sum\\limits_{j\\in{\\mathbb{Z}}}c_i(j)\\phi_i(\\cdot-j)  \\Big| {c_i(j)}_{j\\in{\\mathbb{Z}}}\\in\\ell^p_{\\mu}, i=1,...,r\\Big}, p\\in[1,\\infty],] and generates a closed shift-invariant subspace of $L^p_\\mu(\\mathbb{R})$. The first construction is obtained by choosing functions $\\phi_i$, $i=1,...,r$, with compactly supported Fourier transforms $\\hat{\\phi}_i$, $i=1,...,r$. The second construction, with compactly supported $\\phi_i,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3285","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"}