A Banach algebra with its applications over paths of bounded variation

Document Type: Original Article


Department of Mathematics‎, ‎Kyonggi University‎, ‎Suwon 16227‎, ‎Republic of Korea


‎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.