Generalized Fourier-Feynman transforms, convolution products, and first variations on function space

DOI10.1216/RMJ-2010-40-3-761zbMath1202.60133OpenAlexW2043782615MaRDI QIDQ983489

David Skoug, Jae Gil Choi, Seung Jun Chang

Publication date: 23 July 2010

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2010-40-3-761

zbMATH Keywords

convolution productfirst variationgeneralized analytic Feynman integralGeneralized Brownian motiongeneralized Fourier-Feynman transform

Mathematics Subject Classification ID

Brownian motion (60J65) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (8)

Effect of drift of the generalized Brownian motion process: an example for the analytic Feynman integral ⋮ Generalized conditional transform with respect to the Gaussian process on function space ⋮ A Cameron-Storvick type theorem on $C_{a,b}^2[0,T$ with applications] ⋮ Some basic relationships among transforms, convolution products, first variations and inverse transforms ⋮ Generalized analytic Fourier-Feynman transform of functionals in a Banach algebra \(\mathcal F^{a,b}_{A_{1},A_{2}}\) ⋮ Sequential generalized transforms on function space ⋮ Unnamed Item ⋮ Rotation of Gaussian processes on function space

Cites Work

• An \(L_2\) analytic Fourier-Feynman transform
• Scale-invariant measurability in Wiener space
• An \(L_p\) analytic Fourier-Feynman transform
• Relationships among transforms, convolutions, and first variations
• Generalized transforms and convolutions
• Convolution and the Fourier-Wiener transform on abstract Wiener space
• Convolution in Fourier-Wiener transform
• Fourier-feynman transform, convolution and first variation of functional on abstract wiener
• Analytic Fourier-Feynman Transforms and Convolution
• Generalized Fourier-Feynman transforms and a first variation on function space
• Integration by parts formulas involving generalized Fourier-Feynman transforms on function space
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