{"paper":{"title":"Semiclassical expansion for exactly solvable differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Boris Shapiro, Jorge A. Borrego-Morell","submitted_at":"2024-02-29T12:12:42Z","abstract_excerpt":"Below we study a linear differential equation $\\MM (v(z,\\eta))=\\eta^M{v(z,\\eta)}$, where $\\eta>0$ is a large spectral parameter and $\\MM=\\sum_{k=1}^{M}\\rho_{k}(z)\\frac{d^k}{dz^k},\\; M\\ge 2$ is a differential operator with polynomial coefficients such that the leading coefficient $\\rho_M(z)$ is a monic complex-valued polynomial with $\\dgr{\\rho_M }=M$ and other $\\rho_k(z)$'s are complex-valued polynomials with $\\dgr{\\rho_k }\\leq k$. We prove the Borel summability of its WKB-solutions in the Stokes regions. For $M=3$ under the assumption that $\\rho_M$ has simple zeros, we give the full descriptio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.19087","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/2402.19087/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"}