Abstract
We consider a particular Fourier integral operator with folding canonical relations, which arises in scattering theory: the Radon Transform of Melrose and Taylor. We obtain the regularity properties of this operator when the obstacle admits tangent planes with contact of precise order k (Theorem 1.1 and its Corollary). For these purposes, we derive asymptotic estimates for oscillatory integral operators in Wn with folding canonical relations (Theorem 2.2). Asymptotics correspond to vanishing principal curvature of a fold of one of the projections from the canonical relation, and to small support of the localization of oscillatory integral operator.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
