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East Asian Mathematical Journal
Article . 2013 . Peer-reviewed
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FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FOURIER-TYPE FUNCTIONALS ON WIENER SPACE

Authors: Byoung Soo Kim;

FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FOURIER-TYPE FUNCTIONALS ON WIENER SPACE

Abstract

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
bronze