Characterization for the spectrum of the hypergeometric Fourier transform in terms of the generalized resolvent function

摘要

In this paper, we consider the generalized Poisson's equation associated with Heckman-Opdam Laplacian operator. We introduce and we study the generalized resolvent function associated to the equation. Next, we characterize the spectrum of the hypergeometric Fourier transform via the generalized resolvent function.