Some Properties of the Double Laplace Transformation
Geraldine A. Coon, Dorothy L. Bernstein · Transactions of the American Mathematical Society · 1953
This paper considers the Stieltjes integral fQe~"x~lyd (x, y) ; the transform we consider is a special case of this when {x, y)=fRXY^(x> y)d{x, y). JoOn defining /» x y» X /* x N(x, y) = I Ty(u, y)du, 0(x, y) = I F(u, y)du, H0(x) = j H(u)du, Jo Jo Jo N and 0 are in 2,(1.17) 0(x, y) = Ho(x) + f Fv(u, v)d(u, v) = H0(x) + f N(x, v)dv, J (0,0) J 0