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Advances in Operator Theory
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Cho, D. (2018). A Banach algebra with its applications over paths of bounded variation. Advances in Operator Theory, 3(4), 794-806. doi: 10.15352/aot.1802-1310
Dong Hyun Cho. "A Banach algebra with its applications over paths of bounded variation". Advances in Operator Theory, 3, 4, 2018, 794-806. doi: 10.15352/aot.1802-1310
Cho, D. (2018). 'A Banach algebra with its applications over paths of bounded variation', Advances in Operator Theory, 3(4), pp. 794-806. doi: 10.15352/aot.1802-1310
Cho, D. A Banach algebra with its applications over paths of bounded variation. Advances in Operator Theory, 2018; 3(4): 794-806. doi: 10.15352/aot.1802-1310

A Banach algebra with its applications over paths of bounded variation

Article 4, Volume 3, Issue 4 - Serial Number 10, Autumn 2018, Page 794-806  XML PDF (120.95 K)
Document Type: Original Article
DOI: 10.15352/aot.1802-1310
Author
Dong Hyun Cho email
Department of Mathematics‎, ‎Kyonggi University‎, ‎Suwon 16227‎, ‎Republic of Korea
Receive Date: 11 February 2018,  Revise Date: 07 May 2018,  Accept Date: 14 May 2018 
Abstract
‎Let $C[0,T]$ denote the space of continuous‎, ‎real-valued functions on $[0,T]$‎. ‎In this paper we introduce two Banach algebras‎: ‎one of them is defined on $C[0,T]$ and the other is a space of equivalence classes of measures over paths of bounded variation on $[0,T]$‎. ‎We establish an isometric isomorphism between them‎, ‎and evaluate analytic Feynman integrals of the functions in the Banach algebras which play significant roles in the Feynman integration theories and quantum mechanics‎.
Keywords
Banach algebra; Feynman integral; Ito integral; Paley-Wiener-Zygmund integral; Wiener space
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