Analogies from Complex Analysis and Heat Conduction for Wave Propagation

Source abstract

D. V. Widder [Arch. Rational Mech. Anal., 21(1966), pp. 108–119] showed that solutions of the heat equation share many of the properties of solutions of Laplace’s equation, i.e., of analytic functions. In this paper, we show that those analogues extend to solutions of the wave equation. They include representation of a solution as a convolution transform or in a series of polynomials, and extend Widder’s list of properties to include the wave equation with remarkable similarity.