INTEGRAL TRANSFORMS OF FUNCTIONALS ON A FUNCTION SPACE OF TWO VARIABLES

We establish the various relationships among the integral transform FαβF, the convolution product (F*G)α and the first variation δF for a class of functionals defined on K(Q), the space of complex-valued continuous functions on Q = [0, S]× [0, T]which satisfy x(s, 0) = x(0, t) = 0 for all (s, t) ∈Q. And also we obtain Parseval's and Plancherel's relations for the integral transform of some functionals de¯ned on K(Q).