{"paper":{"title":"Pointwise Convergence of Schr\\\"{o}dinger Operators in Bessel Potential Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiheng Tan, Wenchang Sun, Yucheng Pan","submitted_at":"2026-05-25T13:29:54Z","abstract_excerpt":"We study the pointwise convergence of solutions to the free Schr\\\"{o}dinger equation with initial data in the Bessel potential spaces $L_s^p(\\mathbb{R}^n)$. We establish new sufficient regularity indices for pointwise convergence across the full range $1 \\leq p < \\infty$, and demonstrate via counterexamples that these indices are sharp for all $1 \\leq p \\leq 2$ in one dimension, as well as at the endpoint $p=1$ and $p>2+p_n$ in higher dimensions. The proofs rely on the high-dimensional stationary phase method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25833","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25833/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}