{"paper":{"title":"Global L2-Boundedness Theorems for Semiclassical Fourier Integral Operators with Complex Phase","license":"","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Torben Swart, Vidian Rousse","submitted_at":"2007-10-23T07:49:33Z","abstract_excerpt":"In this work, a class of semiclassical Fourier Integral Operators (FIOs) with complex phase associated to some canonical transformation of the phase space $T^*\\R^d$ is constructed. Upon some general boundedness assumptions on the symbol and the canonical transformation, their continuity (as operators) from the Schwartz class into itself and from $L^2$ into itself are proven."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.4200","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"}