{"paper":{"title":"Scalar spectral measures associated with an Operator-Fractal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.SP","authors_text":"Karen L. Shuman, Keri A. Kornelson, Palle E. T. Jorgensen","submitted_at":"2012-04-23T17:15:19Z","abstract_excerpt":"We examine the operator $U_5$ defined on $L^2(\\mu_{\\frac14})$ where $\\mu_{\\frac14}$ is the 1/4 Cantor measure. The operator $U_5$ scales the elements of the canonical exponential spectrum for $L^2(\\mu_{\\frac14})$ by 5 --- that is, $Ue_{\\gamma} = e_{5\\gamma}$ where $e_{\\gamma}(t) = e^{2\\pi i \\gamma t}$. It is known that $U_5$ has a self-similar structure, which makes its spectrum, which is currently unknown, of particular interest. In order to better understand the spectrum of $U_5$, we demonstrate a decomposition of the projection valued measures and scalar spectral measures associated with $U"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5116","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"}