{"paper":{"title":"Spectral dimensions of Krein-Feller operators in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.SP","authors_text":"Aljoscha Niemann, Marc Kesseb\\\"ohmer","submitted_at":"2022-02-10T18:52:04Z","abstract_excerpt":"We study the spectral dimensions of Krein-Feller operators for arbitrary for arbitrary finite Borel measures $\\nu$ on the $d$-dimensional unit cube ($d\\geq2$) via a form approach. We make use of the spectral partition function of $\\nu$ as introduced in [Kesseb\\\"ohmer and Niemann, Exact asymptotic order for adaptive approximations. 2023, arXiv:2312.16644] and, assuming that the lower $\\infty$-dimension of $\\nu$ exceeds $d-2$, we identify the upper Neumann spectral dimension as the unique zero of the spectral partition function, thus revealing the intrinsic connection of these spectral and fract"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.05247","kind":"arxiv","version":5},"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/2202.05247/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"}