Integral transforms in linear equations of parabolic type with constant coefficients

Abstract

Let u be a function of the Euclidean space Eⁿ of n dimensions, let be the symbolic vector and let

be a polynomial inthe vector Lε Eⁿ with constant coefficients. We con sider the differential equation

of parabolic type. For the fundamental solution K(x,t) of this equation, we consider the Poisson integral formula

and investigate the relationship between ø(y)and u(x,t) following a general theory of integral transforms