{"paper":{"title":"Spectral regularity with respect to dilations for a class of pseudodifferential operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Horia D. Cornean, Radu Purice","submitted_at":"2024-11-22T09:50:03Z","abstract_excerpt":"We continue the study of the perturbation problem discussed in \\cite{CP3} and get rid of the 'slow variation' assumption by considering symbols of the form $a\\big(x+\\delta\\,F(x),\\xi\\big)$ with $a$ a real H\\\"{o}rmander symbol of class $S^0_{0,0}(\\mathbb{R}^d\\times\\mathbb{R}^d)$ and $F$ a smooth function with all its derivatives globally bounded, with $|\\delta|\\leq1$. We prove that while the Hausdorff distance between the spectra of the Weyl quantization of the above symbols in a neighbourhood of $\\delta=0$ is still of the order $\\sqrt{|\\delta|}$, the distance between their spectral edges behave"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14824","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/2411.14824/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"}