{"paper":{"title":"Fredholm Properties and $L^p$-Spectra of Localized Rotating Waves in Parabolic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Denny Otten, Wolf-J\\\"urgen Beyn","submitted_at":"2016-12-22T10:44:48Z","abstract_excerpt":"In this paper we study spectra and Fredholm properties of Ornstein-Uhlenbeck operators $$\\mathcal{L}v(x)=A\\triangle v(x)+\\langle Sx,\\nabla v(x)\\rangle+Df(v_{\\star}(x))v(x),\\,x\\in\\mathbb{R}^d,\\,d\\geqslant 2$$ where $v_{\\star}:\\mathbb{R}^d\\rightarrow\\mathbb{R}^m$ is a rotating wave profile with $v_{\\star}(x)\\to v_{\\infty}\\in\\mathbb{R}^m$ as $|x|\\to\\infty$, $f:\\mathbb{R}^m\\rightarrow\\mathbb{R}^m$ is smooth, $A\\in\\mathbb{R}^{m,m}$ has eigenvalues with positive real parts and commutes with the limit matrix $Df(v_{\\infty})$. The matrix $S\\in\\mathbb{R}^{d,d}$ is assumed to be skew-symmetric with eige"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07535","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":""},"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"}