Exact propagators for some degenerate hyperbolic operators

Abstract

Exact propagators are obtained for the degenerate second order hyperbolic operators ∂²_t-t^2lΔ_x, l=1,2,..., by analytic continuation from the degenerate elliptic operators ∂²_t+t^2lΔ_x. The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.