{"paper":{"title":"Spectral Meromorphic Operators and Nonlinear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.FA","authors_text":"(2) University of Maryland at College Park, Moscow, Moscow), P. G. Grinevich (1), Russia, S.Novikov (2) ((1) Landau Institute for Theoretical Physics, Steklov Math Institute, USA","submitted_at":"2014-09-22T21:38:25Z","abstract_excerpt":"We study here class of 1D spectral-meromorphic (s-meromorphic) OD operators $L=\\partial_x^n+\\sum_{n-2\\geq i\\geq 0}a_{n-2-i}\\partial_x^i$ with meromorphic coefficients $a_j$ near $x\\in R$ such that all eigenfunctions $L\\psi=\\alpha\\psi$ are $x$--meromorphic near $x\\in R$ for all $\\alpha$. Symmetric $s$-meromorphic operators are self-adjoint with respect to indefinite inner product well-defined for some special spaces of singular functions. In particular, all algebraic operators $L$--i.e. operators entering Burchnall-Chaundy-Krichever (BChK) rank one commutative rings -- are s-meromorphic. For Kd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6349","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":""},"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"}