Banach Journal of Mathematical Analysis

Multiple generalized analytic Fourier--Feynman transform via rotation of Gaussian paths on function space

Seung Jun Chang, Jae Gil Choi, and Ae Young Ko

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Abstract

The main purpose of this article is to develop the generalized analytic Fourier--Feynman transform theory. We introduce a generalized analytic Fourier--Feynman transform and a multiple generalized analytic Fourier--Feynman transform with respect to Gaussian processes on the function space $C_{a,b}[0,T]$ induced by a generalized Brownian motion process. We then establish a relationship between these two generalized analytic transforms.

Article information

Source
Banach J. Math. Anal., Volume 9, Number 4 (2015), 58-80.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1429286057

Digital Object Identifier
doi:10.15352/bjma/09-4-4

Mathematical Reviews number (MathSciNet)
MR3336883

Zentralblatt MATH identifier
1327.46044

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

Keywords
Generalized Brownian motion process Gaussian process generalized analytic Feynman integral generalized analytic Fourier--Feynman transform multiple generalized analytic Fourier--Feynman transform

Citation

Chang, Seung Jun; Choi, Jae Gil; Ko, Ae Young. Multiple generalized analytic Fourier--Feynman transform via rotation of Gaussian paths on function space. Banach J. Math. Anal. 9 (2015), no. 4, 58--80. doi:10.15352/bjma/09-4-4. https://projecteuclid.org/euclid.bjma/1429286057


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