Abstract
We present the solution of the Cauchy problem (the initial-value problem in the whole space) for the wave equation with infinite-dimensional Levy Laplacian ΔL, $$ \frac{{\partial ^2 U(t,x)}} {{\partial t^2 }} = \Delta _L U(t,x) $$ in two function classes, the Shilov class and the Gâteaux class.
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