{"paper":{"title":"An Operator-Fractal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.OA","authors_text":"Karen L. Shuman, Keri A. Kornelson, Palle E. T. Jorgensen","submitted_at":"2011-09-14T18:58:51Z","abstract_excerpt":"Certain Bernoulli convolution measures (\\mu) are known to be spectral. Recently, much work has concentrated on determining conditions under which orthonormal Fourier bases (i.e. spectral bases) exist. For a fixed measure known to be spectral, the orthonormal basis need not be unique; indeed, there are often families of such spectral bases.\n  Let \\lambda = 1/(2n) for a natural number n and consider the Bernoulli measure (\\mu) with scale factor \\lambda. It is known that L^2(\\mu) has a Fourier basis. We first show that there are Cuntz operators acting on this Hilbert space which create an orthogo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3168","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":""},"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"}