Research announcement asymptotics of pdo on discontinuous functions near singular support

Abstract

Let β be a pseudo-differential operator (PDO) with a real-valued symbol satisfying asymptotic condition where b is a strictly positive C^∞ function on the unit sphere in R². Let Ff denote the Fourier transform of f . We consider the action of the PDO on functions with discontinuities and analyze the asymptotic behavior of B f in a neighborhood of a discontinuity curve S of f . Applicationsof the obtained results in computer tomography are illustrated.