Generalized transforms and generalized convolution products associated with Gaussian paths on function space

Seung Jun Chang; Jae Gil Choi

doi:10.3934/cpaa.2020019

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2020, Volume 19, Issue 1: 371-389. Doi: 10.3934/cpaa.2020019

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Generalized transforms and generalized convolution products associated with Gaussian paths on function space

Seung Jun Chang and
Jae Gil Choi^,

Department of Mathematics, Dankook University, Cheonan 330-714, Republic of Korea

^* Corresponding author
^* Corresponding author

Received: November 30, 2018

Revised: March 31, 2019

Published: July 2019

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Abstract

In this paper we define a more general convolution product (associated with Gaussian processes) of functionals on the function space $ C_{a, b}[0, T] $. The function space $ C_{a, b}[0, T] $ is induced by a generalized Brownian motion process. Thus the Gaussian processes used in this paper are non-centered processes. We then develop the fundamental relationships between the generalized Fourier–Feynman transform associated with the Gaussian process and the convolution product.

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Mathematics Subject Classification: Primary: 28C20, 60G15, 60J65; Secondary: 46B09, 42B10, 46G12.

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