{"paper":{"title":"Counterexamples to the Kotani-Last Conjecture for Continuum Schr\\\"odinger Operators via Character-Automorphic Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"David Damanik (Rice University), Peter Yuditskii (Johannes Kepler Universit\\\"at Linz)","submitted_at":"2014-05-24T20:57:14Z","abstract_excerpt":"The Kotani-Last conjecture states that every ergodic operator in one space dimension with non-empty absolutely continuous spectrum must have almost periodic coefficients. This statement makes sense in a variety of settings; for example, discrete Schr\\\"odinger operators, Jacobi matrices, CMV matrices, and continuum Schr\\\"odinger operators.\n  In the main body of this paper we show how to construct counterexamples to the Kotani-Last conjecture for continuum Schr\\\"odinger operators by adapting the approach developed by Volberg and Yuditskii to construct counterexamples to the Kotani-Last conjectur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6343","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"}