{"paper":{"title":"Decay estimates for a class of Dunkl wave equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Cheng Luo, Manli Song, Shyam Swarup Mondal","submitted_at":"2024-07-09T15:30:18Z","abstract_excerpt":"Let $\\Delta_\\kappa$ be the Dunkl Laplacian on $\\mathbb{R}^n$ and $\\phi: \\mathbb{R}^+ \\to \\mathbb{R}$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay estimate for a class of dispersive semigroup of the form $e^{it\\phi(\\sqrt{-\\Delta_\\kappa})}$.W e overcome the difficulty arising from the non-homogeneousity of $\\phi$ by frequency localization. As applications, in the next part of the paper, we establish Strichartz estimates for some concrete wave equations associated with the Dunkl Laplacian $\\Delta_k,$ which corresponds to $\\phi(r)=r, r^2, r^2+r^4, \\sqrt{1+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06949","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/2407.06949/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"}