A Banach algebra similar to Cameron-Storvick's one with its equivalent spaces (Q1644421)

Summary: 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 \(\mathbb{C}\)-valued, and finite Borel measures on \(L^2 [0, T]\). 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.