On the spectrum of the distributional kernel related to the residue

Abstract

We study the spectrum of the distributional kernel Kα,β(x), where α and β are complex numbers and x is a point in the space ℝn of the n‐dimensional Euclidean space. We found that for any nonzero point ξ that belongs to such a spectrum, there exists the residue of the Fourier transform , where α = β = 2k, k is a nonnegative integer and ξ ∈ ℝn.