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
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.
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