{"paper":{"title":"A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Frank R\\\"osler, Patrick Dorey, Patrick W. Dondl","submitted_at":"2015-05-21T13:09:48Z","abstract_excerpt":"We are concerned with the non-normal Schr\\\"odinger operator $$\n  H=-\\Delta+V $$ on $ L^2(\\mathbb R^n)$, where $V\\in W^{1,\\infty}_{\\text{loc}}(\\mathbb{R}^n)$ and $\\operatorname{Re} (V(x))\\ge c|x|^2-d$ for some $c,d>0$. The spectrum of this operator is discrete and contained in the positive half plane. In general, the $\\varepsilon$-pseudospectrum of $H$ will have an unbounded component for any $\\varepsilon>0$ and thus will not approximate the spectrum in a global sense. By exploiting the fact that the semigroup $e^{-tH}$ is immediately compact, we show a complementary result, namely that for eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05719","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}