A Banach Algebra Similar to Cameron-Storvick’s One with Its Equivalent Spaces

Dong Hyun Cho

doi:10.1155/2018/9345126

Abstract

Let C[0,T] denote an analogue of a generalized Wiener space, that is, the space of continuous, real-valued functions on the interval [0,T]. In this paper, we introduce a Banach algebra on C[0,T] which generalizes Cameron-Storvick’s one, the space of generalized Fourier-Stieltjes transforms of the C-valued, and finite Borel measures on L2[0,T]. We also investigate properties of the Banach algebra on C[0,T] and equivalence between the Banach algebra and the Fresnel class which plays a significant role in Feynman integration theories and quantum mechanics.

Highlights

Let C0[0, T] denote the Wiener space, that is, the space of continuous, real-valued functions x on the interval [0, T] with x(0) = 0
We introduce a Banach algebra on C[0, T] which generalizes Cameron-Storvick’s one, the space of generalized Fourier-Stieltjes transforms of the C-valued, and finite Borel measures on L2[0, T]
We investigate properties of the Banach algebra on C[0, T] and equivalence between the Banach algebra and the Fresnel class which plays a significant role in Feynman integration theories and quantum mechanics

Summary

A Banach Algebra Similar to Cameron-Storvick’s One with Its Equivalent Spaces

Received 5 February 2018; Revised 6 April 2018; Accepted 16 April 2018; Published 3 June 2018. Let C[0, T] denote an analogue of a generalized Wiener space, that is, the space of continuous, real-valued functions on the interval [0, T]. We introduce a Banach algebra on C[0, T] which generalizes Cameron-Storvick’s one, the space of generalized Fourier-Stieltjes transforms of the C-valued, and finite Borel measures on L2[0, T]. We investigate properties of the Banach algebra on C[0, T] and equivalence between the Banach algebra and the Fresnel class which plays a significant role in Feynman integration theories and quantum mechanics

Introduction

An Analogue of a Generalized Wiener Space

A Banach Algebra with Its Applications

The Fresnel Class with Its Equivalent Spaces

Conflicts of Interest