{"paper":{"title":"Hermite Multipliers on Modulation Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Divyang G. Bhimani, Rakesh Balhara, Sundaram Thangavelu","submitted_at":"2017-12-09T09:45:48Z","abstract_excerpt":"We study multipliers associated to the Hermite operator $H=-\\Delta + |x|^2$ on modulation spaces $M^{p,q}(\\mathbb R^d)$. We prove that the operator $m(H)$ is bounded on $M^{p,q}(\\mathbb R^d)$ under standard conditions on $m,$ for suitable choice of $p$ and $q$. As an application, we point out that the solutions to the free wave and Schr\\\"odinger equations associated to $H$ with initial data in a modulation space will remain in the same modulation space for all times. We also point out that Riesz transforms associated to $H$ are bounded on some modulation spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03364","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"}