Asymptotic behaviour of a class of singular Fourier Integrals

This paper presents the asymptotic expansion, with respect to the large real parameter λ, of the singular Fourier integral I(λ) :=fp ∫₀^b K(x, λx)e^iλx dx, where 0 < b ≤ + ∞, the symbol fp designates an integration in the finite part sense of Hadamard and complex function K(x, u) belongs to a specific set of pseudofunctions which may present a singular behaviour of logarithmic nature at the endpoints.