{"paper":{"title":"Isomorphism in Wavelets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Wei Huang, Xingde Dai","submitted_at":"2019-04-15T15:45:41Z","abstract_excerpt":"Two scaling functions $\\varphi_A$ and $\\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\\varphi_A \\simeq \\varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be $d\\times d$ and $s\\times s$ \\thematrix matrices with $d, s\\geq 1$ respectively and let $\\varphi_A$ be a scaling function associated with matrix $A$ and generated by a finite solution. There always exists a scaling function $\\varphi_B$ associated with matrix $B$ such that \\begin{equation*}\n  \\varphi_B \\simeq \\varphi_A. \\end{equation*} An example shows that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07139","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"}