{"paper":{"title":"Projections and Dyadic Parseval Frame MRA Wavelets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Edward N. Wilson, Guido L. Weiss, Peter M. Luthy","submitted_at":"2014-09-24T01:04:28Z","abstract_excerpt":"A classical theorem attributed to Naimark states that, given a Parseval frame $\\mathcal{B}$ in a Hilbert space $\\mathcal{H}$, one can embed $\\mathcal{H}$ in a larger Hilbert space $\\mathcal{K}$ so that the image of $\\mathcal{B}$ is the projection of an orthonormal basis for $\\mathcal{K}$. In the present work, we revisit the notion of Parseval frame MRA wavelets from two papers of Paluszy\\'nski, \\v{S}iki\\'c, Weiss, and Xiao (PSWX) and produce an analog of Naimark's theorem for these wavelets at the level of their scaling functions. We aim to make this discussion as self-contained as possible an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6786","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"}