{"paper":{"title":"Sharp spectral stability for a class of singularly perturbed pseudo-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Horia D. Cornean, Radu Purice","submitted_at":"2023-02-28T22:28:50Z","abstract_excerpt":"Let $a(x,\\xi)$ be a real H\\\"ormander symbol of the type $S_{0,0}^0(\\mathbb{R}^{d}\\times \\mathbb{R}^d)$, let $F$ be a smooth function with all its derivatives globally bounded, and let $K_\\delta$ be the self-adjoint Weyl quantization of the perturbed symbols $a(x+F(\\delta\\, x),\\xi)$, where $|\\delta|\\leq 1$. First, we prove that the Hausdorff distance between the spectra of $K_\\delta$ and $K_{0}$ is bounded by $\\sqrt{|\\delta|}$, and we give examples where spectral gaps of this magnitude can open when $\\delta\\neq 0$. Second, we show that the distance between the spectral edges of $K_\\delta$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.00112","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.00112/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"}