
Abstract. We develop a Fourier-Feynman theory for Fourier-type func-tionals k F and [F on Wiener space. We show that Fourier-Feynmantransform and convolution of Fourier-type functionals exist. We alsoshow that the Fourier-Feynman transform of the convolution product ofFourier-type functionals is a product of Fourier-Feynman transforms ofeach functionals. 1. Introduction and preliminariesLet C 0 [0;T] denote the Wiener space, that is, the space of real valuedcontinuous functions xon [0;T] with x(0) = 0. Let Mdenote the class ofall Wiener measurable subsets of C 0 [0;T] and let mdenote Wiener measure.(C 0 [0;T];M;m) is a complete measure space and we denote the Wiener integralof a functional FbyZ C 0 [0;T] F(x)dm(x):A subset Eof C 0 [0;T] is said to be scale-invariant measurable provided ˆEis Wiener measurable for every ˆ>0, and a scale-invariant measurable setN is said to be scale-invariant null provided m(ˆN) = 0 for every ˆ>0. Aproperty that holds except on a scale-invariant null set is said to hold scale-invariant almost everywhere (s-a.e.). Given two complex-valued functions Fand Gon C
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