ASYMPTOTIC-BEHAVIOR OF THE FOURIER-TRANSFORM OF PIECEWISE-SMOOTH FUNCTIONS

Let D be a bounded domain in R(n) such that partial derivative D is a union of a finite number of smooth hypersurfaces in general position. The asymptotics of the Fourier transform of a piecewise smooth function f (x) with discontinuities of the first kind on partial derivative D, in particular of the characteristic function of D, is found in almost all directions. The results are based on our recent work on the singularities of the Radon transform.