Oscillatory integral operators in scattering theory Academic Article

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 n 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.

authors

• Comech, Andrew

published proceedings

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

• Comech, A.

complete list of authors

• Comech, A

publication date

• December 1997

published in

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS  Journal

start page

• 841

end page

• 867

volume

• 22

issue

• 5-6