{"paper":{"title":"Schr\\\"odinger type propagators, pseudodifferential operators and modulation spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Anita Tabacco, Elena Cordero, Patrik Wahlberg","submitted_at":"2012-07-09T16:44:50Z","abstract_excerpt":"We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schr\\\"odinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents $p,q,r_1,r_2,t_1,t_2 \\in [1,\\infty]$ of modulation spaces such that a symbol in $M^{p,q}(\\mathbb R^{2d})$ gives a pseudodifferential operator that is continuous from $M^{r_1,r_2}(\\mathbb R^d)$ into $M^{t_1,t_2}(\\mathbb R^d)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2099","kind":"arxiv","version":3},"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"}