INTEGRAL TRANSFORMS OF FUNCTIONALS ON A FUNCTION SPACE OF TWO VARIABLES

Abstract

We establish the various relationships among the integral transform Fα,βF , 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 defined on K(Q).

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