{"paper":{"title":"On $m$-order logarithmic Schr\\\"odinger operator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Estefan\\'ia Dalmasso, Jorge J. Betancor, Lourde Rodr\\'iguez-Mesa, Pablo Quijano","submitted_at":"2026-06-19T02:48:01Z","abstract_excerpt":"In this paper we study the logarithm of order $m$ of the Schr\\\"odinger operator $\\mathcal L_V$ in $\\mathbb R^d$, for certain nonnegative potentials $V$. First, the operator $\\log^m\\mathcal L_V$, $m\\in \\mathbb N$, is defined by using the spectral measure associated with the self-adjoint operator $\\mathcal L_V$ on a suitable subspace of $L^2(\\mathbb R^d)$. Then, the semigroup of operators $\\{T_t^V\\}_{t>0}$ generated by $\\mathcal L_V$ allows us to extend the definition of $\\log^m\\mathcal L_V$ to a wider class of Lipschitz functions. By using logarithmic operators $\\log^m\\mathcal L_V$, $m\\in \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21056","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21056/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"}