Some General Formulas for Double Laplace Transformations
Geraldine A. Coon, Dorothy L. Bernstein · Proceedings of the American Mathematical Society · 1963
In many problems amenable to double Laplace transformations it is necessary to perform certain operations upon the functions involved.This paper studies the effects of such operations upon the transforms.The one-and two-dimensional transforms are defined by L. [H] =fo~e-"H(x)dx and L [F] =fQ.e-,x-">F(x, y)d(x, y) where Q is the open first quadrant and s and t are complex variables: s = ff+ik, t = T+in.The transforms are denoted by h(s) and f(s, t).It is assumed that L[F] converges boundedly rather than absolutely; various types of convergence are defined in [l].