On Some Solutions to the Klein-Gordon Equation Related to an Integral of Sonine

Abstract

An integral due to Sonine is used to obtain an expansion for special solutions of the Klein-Gordon equation. This expansion is used to estimate the norms <!-- MATH $\left\|W( \cdot ,t)\right\|_p$ --> as <!-- MATH $t \to \infty$ --> . These estimates yield results on the time decay of a fairly wide class of solutions to the Klein-Gordon equation.