Abstract
In this paper we use generalized Fourier-Hermite functionals to obtain a complete orthonormal set in L2(Ca,b[0,T]) where Ca,b[0,T] is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in L2(Ca,b[0,T]) has an integral transform ℱγ,βF also belonging to L2(Ca,b[0,T]).
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