{"paper":{"title":"Convergence of a Class of Schr\\\"{o}dinger Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dan Li, Haixia Yu","submitted_at":"2019-06-12T14:01:12Z","abstract_excerpt":"In this paper, we set up the selection conditions for time series $\\{t_k\\}_{k=1}^\\infty$ which converge to 0 as $k\\rightarrow\\infty$ such that the solutions of a class of generalized Schr\\\"odinger equations almost everywhere pointwise converge to their initial data in $H^s(\\mathbb{R}^n)$ for $s>0$. As it is known that the pointwise convergence can not be true for Schr\\\"odinger equation when $s<\\frac{n}{2(n+1)}$ as $t\\rightarrow0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05145","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"}