{"paper":{"title":"W-Markov measures, transfer operators, wavelets and multiresolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Alpay, Izchak Lewkowicz, Palle Jorgensen","submitted_at":"2016-06-24T14:08:43Z","abstract_excerpt":"In a general setting we solve the following inverse problem: Given a positive operators $R$, acting on measurable functions on a fixed measure space $(X,\\mathcal B_X)$, we construct an associated Markov chain. Specifically, starting with a choice of $R$ (the transfer operator), and a probability measure $\\mu_0$ on $(X, \\mathcal B_X)$, we then build an associated Markov chain $T_0, T_1, T_2,\\ldots$, with these random variables (r.v) realized in a suitable probability space $(\\Omega,\\mathcal F, \\mathbb P)$, and each r.v. taking values in $X$, and with $T_0$ having the probability $\\mu_0$ as law."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07692","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"}