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January 2019 Translation theorems for the Fourier–Feynman transform on the product function space C a , b 2 [ 0 , T ]
Seung Jun Chang, Jae Gil Choi, David Skoug
Banach J. Math. Anal. 13(1): 192-216 (January 2019). DOI: 10.1215/17358787-2018-0022

Abstract

In this article, we establish the Cameron–Martin translation theorems for the analytic Fourier–Feynman transform of functionals on the product function space C a , b 2 [ 0 , T ] . The function space C a , b [ 0 , T ] is induced by the generalized Brownian motion process associated with continuous functions a ( t ) and b ( t ) on the time interval [ 0 , T ] . The process used here is nonstationary in time and is subject to a drift a ( t ) . To study our translation theorem, we introduce a Fresnel-type class F A 1 , A 2 a , b of functionals on C a , b 2 [ 0 , T ] , which is a generalization of the Kallianpur and Bromley–Fresnel class F A 1 , A 2 . We then proceed to establish the translation theorems for the functionals in F A 1 , A 2 a , b .

Citation

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Seung Jun Chang. Jae Gil Choi. David Skoug. "Translation theorems for the Fourier–Feynman transform on the product function space C a , b 2 [ 0 , T ] ." Banach J. Math. Anal. 13 (1) 192 - 216, January 2019. https://doi.org/10.1215/17358787-2018-0022

Information

Received: 27 March 2018; Accepted: 27 June 2018; Published: January 2019
First available in Project Euclid: 6 December 2018

zbMATH: 07002038
MathSciNet: MR3892340
Digital Object Identifier: 10.1215/17358787-2018-0022

Subjects:
Primary: ‎46G12
Secondary: 28C20 , 42B10 , 60J65

Keywords: generalized analytic Feynman integral , generalized analytic Fourier–Feynman transform , Generalized Brownian motion process , generalized Fresnel-type class , translation theorem

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 1 • January 2019
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