Advances in Operator Theory

A Banach algebra with its applications over paths of bounded variation

Dong Hyun Cho

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‎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.

Article information

Adv. Oper. Theory, Volume 3, Number 4 (2018), 794-806.

Received: 11 February 2018
Accepted: 14 May 2018
First available in Project Euclid: 8 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 28C20‎ ‎60H05

Banach algebra ‎Feynman integral‎ ‎Itô integral ‎Paley-Wiener-Zygmund integral ‎Wiener space


Cho, Dong Hyun. A Banach algebra with its applications over paths of bounded variation. Adv. Oper. Theory 3 (2018), no. 4, 794--806. doi:10.15352/aot.1802-1310.

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