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December 2021 Generalized sequential Feynman integral and Fourier–Feynman transform
Il Yoo, Byoung Soo Kim
Rocky Mountain J. Math. 51(6): 2251-2268 (December 2021). DOI: 10.1216/rmj.2021.51.2251

Abstract

We introduce the concepts of a generalized sequential Feynman integral and a generalized sequential Fourier–Feynman transform. Existence theorems of these integral and transform are obtained for functionals in a Banach algebra 𝒮^ and some related functionals. Also we give a simple proof of a translation theorem for generalized sequential Feynman integral. Previous results on sequential Feynman integral and sequential Fourier–Feynman transform can be obtained as corollaries of our results. In the last section we introduce the concept of translation invariant generalized sequential Feynman integral.

Citation

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Il Yoo. Byoung Soo Kim. "Generalized sequential Feynman integral and Fourier–Feynman transform." Rocky Mountain J. Math. 51 (6) 2251 - 2268, December 2021. https://doi.org/10.1216/rmj.2021.51.2251

Information

Received: 31 July 2020; Revised: 17 February 2021; Accepted: 2 April 2021; Published: December 2021
First available in Project Euclid: 22 March 2022

Digital Object Identifier: 10.1216/rmj.2021.51.2251

Subjects:
Primary: 28C20 , ‎46G12

Keywords: Banach algebra 𝒮^ , generalized sequential Feynman integral , generalized sequential Fourier–Feynman transform , translation invariant generalized sequential Feynman integral , translation theorem

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 6 • December 2021
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