{"paper":{"title":"Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sanjoy Pusti, Utsav Dewan","submitted_at":"2025-12-10T14:36:42Z","abstract_excerpt":"In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type $\\mathbb{X}=U/K$, of rank $1$ and $2$ respectively, the Sobolev regularity thresholds for the initial data, $\\alpha >1/2$ and $\\alpha >1$ respectively, are sufficient to obtain pointwise convergence of the solution a.e. on $\\mathbb{X}$. We next focus on $K$-biinvariant initial data for certain special cases of rank $1$, depending on geometric considerations, and prove that the sufficiency of the regularity threshold can be improved down to $\\alpha>1/3$, whereas the phenomenon fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.09689","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.09689/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"}