The Cauchy problem for the wave equation with Lévy Laplacian
Sergio A Albeverio, Ya. I. Belopolskaya, М. Н. Феллер · Mathematical Notes · 2010
We present the solution of the Cauchy problem (the initial-value problem in the whole space) for the wave equation with infinite-dimensional Lévy Laplacian Δ L , $$ \frac{{\partial ^2 U(t,x)}} {{\partial t^2 }} = \Delta _L U(t,x) $$ in two function classes, the Shilov class and the Gâteaux class.