Analytic Fourier-Feynman transforms and convolution

Huffman, Timothy; Park, Chull; Skoug, David

doi:10.1090/S0002-9947-1995-1242088-7

Analytic Fourier-Feynman transforms and convolution
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by Timothy Huffman, Chull Park and David Skoug PDF

Trans. Amer. Math. Soc. 347 (1995), 661-673 Request permission

Abstract:

In this paper we develop an ${L_p}$ Fourier-Feynman theory for a class of functionals on Wiener space of the form $F(x) = f(\int _0^T {{\alpha _1}dx, \ldots ,\int _0^T {{\alpha _n}dx)} }$. We then define a convolution product for functionals on Wiener space and show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms.

References

A functional transform for Feynman integrals similar to the Fourier transform

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