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
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
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
