ASYMPTOTIC-BEHAVIOR OF A CLASS OF SINGULAR FOURIER INTEGRALS

This paper presents the asymptotic ic expansion, with respect to the l arge real parameter lambda, of the singular Fourier integral I(lambda) :=fp integral(0)(b)K(x,lambda x)e(i lambda x)dx, where 0 < b, less tha n or equal to + infinity, the symbol f(p) designates an integration in the finite part sense of Hadamard and complex function K(x, u) belong s to a specific set of pseudo-functions which may present a singular b ehaviour of logarithmic nature at the endpoints.