Generalized analytic Fourier-Feynman transform of functionals in a Banach algebra \(\mathcal F^{a,b}_{A_{1},A_{2}}\)

DOI10.1155/2013/954098zbMath1331.60095OpenAlexW2004075165WikidataQ59012796 ScholiaQ59012796MaRDI QIDQ2443778

Jae Gil Choi, Seung Jun Chang, David Skoug

Publication date: 8 April 2014

Published in: Journal of Function Spaces and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/954098

zbMATH Keywords

Banach algebraFourier-Feynman transformabstract Wiener spacestochastic integralgeneralized Brownian motion

Mathematics Subject Classification ID

Generalized stochastic processes (60G20) Stochastic integrals (60H05) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Probability theory on linear topological spaces (60B11) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

Related Items (3)

Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral ⋮ A Cameron-Storvick type theorem on $C_{a,b}^2[0,T$ with applications] ⋮ Translation theorems for the Fourier-Feynman transform on the product function space \(C_{a,b}^2[0,T\)]

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized Fourier-Feynman transforms, convolution products, and first variations on function space
• Integral transforms of functionals in \(L^{2}(C_{a,b}[0,T)\)]
• Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula
• Notes on the Feynman integral. III: The Schrödinger equation
• Conditional function space integrals with applications
• Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments
• A change of scale formula for a function space integral on $C_{a,b}[0,T$]
• GENERALIZED FOURIER-FEYNMAN TRANSFORM AND SEQUENTIAL TRANSFORMS ON FUNCTION SPACE
• Evaluation Formulas for Conditional Function Space Integrals I
• The equivalence of two approaches to the Feynman integral
• Generalized Fourier-Feynman transforms and a first variation on function space
• Parts formulas involving conditional generalized Feynman integrals and conditional generalized Fourier–Feynman transforms on function space
• Functions in the Fresnel Class
• Integration by parts formulas involving generalized Fourier-Feynman transforms on function space

This page was built for publication: Generalized analytic Fourier-Feynman transform of functionals in a Banach algebra \(\mathcal F^{a,b}_{A_{1},A_{2}}\)