{"paper":{"title":"Existence of the Bedrosian Identity for Singular Integral Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Haizhang Zhang, Rongrong Lin","submitted_at":"2014-07-03T10:48:24Z","abstract_excerpt":"The Hilbert transform $H$ satisfies the Bedrosian identity $H(fg)=fHg$ whenever the supports of the Fourier transforms of $f,g\\in L^2(R)$ are respectively contained in $A=[-a,b]$ and $B=R\\setminus(-b,a)$, $0\\le a,b\\le+\\infty$. Attracted by this interesting result arising from the time-frequency analysis, we investigate the existence of such an identity for a general bounded singular integral operator on $L^2(R^d)$ and for general support sets $A$ and $B$. A geometric characterization of the support sets for the existence of the Bedrosian identity is established. Moreover, the support sets for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0861","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"}