{"paper":{"title":"Factoring Pseudoidentity Matrix Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Florian M. Sebert, Yi Ming Zou","submitted_at":"2011-01-19T23:01:22Z","abstract_excerpt":"The problem of factorization and parametrization of compactly supported biorthogonal wavelets was reduced to that of pseudoidentity matrix pairs by Resnikoff, Tian, and Wells in their 2001 paper. Based on a conjecture on the pseudoidentity matrix pairs of rank 2 stated in the same paper, they proved a theorem which gives a complete factorization result for rank 2 compactly supported biorthogonal wavelets. In this paper, we first provide examples to show that the conjecture is not true, then we prove a factorization theorem for pseudoidentity matrix pairs of rank $m\\ge 2$. As a consequence, our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3793","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"}