{"paper":{"title":"Generalized free time-dependent Schr\\\"odinger equation with initial data in Fourier Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Karoline Johansson","submitted_at":"2011-02-15T08:46:03Z","abstract_excerpt":"Consider the solution of the free time-dependent Schr\\\"odinger equation with initial data f. It is shown by Sj\\\"ogren and Sj\\\"olin (1989) that there exists f in the Sobolev space H^s(R^d), s=d/2 such that tangential convergence can not be widened to convergence regions. In 2010 we obtained the corresponding results for a generalized version of the Schr\\\"odinger equation, where -\\Delta_x is replaced by an operator \\phi(D), with special conditions on \\phi. In this paper we show that similar results may be obtained for initial data in Fourier Lebesgue spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2998","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"}