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

Sequential Fourier-feynman Transform, Convolution and First Variation

Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra Ŝ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or co...

Equivalence of K-functionals and modulus of smoothness for fourier transform

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

A Conditional Fourier-feynman Transform and Conditional Convolution Product with Change of Scales on a Function Space I

Abstract. Using a simple formula for conditional expectations over an analogue of Wiener space, we calculate a generalized analytic conditional Fourier-Feynman transform and convolution product of generalized cylinder functions which play important roles in Feynman integration theories and quantum mechanics. We then investigate their relationships, that is, the conditional Fourier-Feynman trans...

Discrete Convolution and the Discrete Fourier Transform

Discrete Convolution First of all we need to introduce what we might call the “wraparound” convention. Because the complex numbers wj = e i 2πj N have the property wj±N = wj, which readily extends to wj+mN = wj for any integer m, and since in the discrete Fourier context we represent all N -dimensional vectors as linear combinations of the Fourier vectors Wk whose components are wkj , we make t...

Discrete integer Fourier transform in real space: elliptic Fourier transform