{"paper":{"title":"Spectrality of Moran-type measures with staggered contraction ratios","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Jing-Cheng Liu, Jun Jason Luo, Lin Mao","submitted_at":"2024-12-18T01:44:30Z","abstract_excerpt":"Consider a Moran-type iterated function system (IFS) \\( \\{\\phi_{k,d}\\}_{d\\in D_{2p_k}, k\\geq 1} \\), where each contraction map is defined as \\[ \\phi_{k,d}(x) = (-1)^d b_k^{-1}(x + d), \\] with integer sequences \\( \\{b_k\\}_{k=1}^\\infty \\) and \\( \\{p_k\\}_{k=1}^\\infty \\) satisfying \\( b_k \\geq 2p_k \\geq 2 \\), and digit sets \\( D_{2p_k} = \\{0, 1, \\ldots, 2p_k - 1\\} \\) for all \\( k \\geq 1 \\). We first prove that this IFS uniquely generates a Borel probability measure \\( \\mu \\). Furthermore, under the divisibility constraints \\[ p_2 \\mid b_2, \\quad 2 \\mid b_2, \\quad \\text{and} \\quad 2p_k \\mid b_k \\ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.13427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}