Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 4 (2017), 785-807.
Analytic Fourier–Feynman transforms and convolution products associated with Gaussian processes on Wiener space
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.
Banach J. Math. Anal., Volume 11, Number 4 (2017), 785-807.
Received: 4 July 2016
Accepted: 1 November 2016
First available in Project Euclid: 30 June 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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