{"paper":{"title":"Spectral property of Cantor measures with consecutive digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chun-kit Lai, Xing-Gang He, Xin-Rong Dai","submitted_at":"2012-09-19T23:26:01Z","abstract_excerpt":"We consider equally-weighted Cantor measures $\\mu_{q,b}$ arising from iterated function systems of the form ${b^{-1}(x+i)}$, $i=0,1,...,q-1$, where $q<b$. We classify the $(q,b)$ so that they have infinitely many mutually orthogonal exponentials in $L^2(\\mu_{q,b})$. In particular, if $q$ divides $b$, the measures have a complete orthogonal exponential system and hence spectral measures. We then characterize all the maximal orthogonal sets $\\Lambda$ when $q$ divides $b$ via a maximal mapping on the $q-$adic tree in which all elements in $\\Lambda$ are represented uniquely in finite $b-$adic expa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4386","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"}