Banach Journal of Mathematical Analysis

Analytic Fourier–Feynman transforms and convolution products associated with Gaussian processes on Wiener space

Seung Jun Chang and Jae Gil Choi

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Abstract

Using Gaussian processes, we define a very general convolution product of functionals on Wiener space and we investigate fundamental relationships between the generalized Fourier–Feynman transforms and the generalized convolution products. Using two rotation theorems of Gaussian processes, we establish that both of the generalized Fourier–Feynman transform of the generalized convolution product and the generalized convolution product of the generalized Fourier–Feynman transforms of functionals on Wiener space are represented as products of the generalized Fourier–Feynman transforms of each functional, with examples.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 4 (2017), 785-807.

Dates
Received: 4 July 2016
Accepted: 1 November 2016
First available in Project Euclid: 30 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1498809807

Digital Object Identifier
doi:10.1215/17358787-2017-0017

Mathematical Reviews number (MathSciNet)
MR3708529

Zentralblatt MATH identifier
1382.28010

Subjects
Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12]
Secondary: 60J65: Brownian motion [See also 58J65] 60G15: Gaussian processes 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
Wiener space Gaussian process generalized analytic Fourier–Feynman transform generalized convolution products

Citation

Chang, Seung Jun; Choi, Jae Gil. Analytic Fourier–Feynman transforms and convolution products associated with Gaussian processes on Wiener space. Banach J. Math. Anal. 11 (2017), no. 4, 785--807. doi:10.1215/17358787-2017-0017. https://projecteuclid.org/euclid.bjma/1498809807


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