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A Fubini theorem for generalized analytic Feynman integrals and Fourier-Feynman transforms on function space
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Abstract
In this paper we use a generalized Brownian motionprocess to define a generalized analytic Feynman integral. We thenestablish a Fubini theorem for the function space integral andgeneralized analytic Feynman integral of a functional F belonging to Banach algebrasab and we proceed to obtain several integration formulas.Finally, we use this Fubini theorem to obtain several Feynmanintegration formulas involving analytic generalizedFourier-Feynman transforms. These results subsume similar knownresults obtained by Huffman, Skoug and Storvick for the standardWiener process.
관련 논문AI추천
Fourier-Feynman transforms for functionals in a generalized Fresnel class유일, 김병수대한수학회 · 대한수학회논문집2007 · 제22권 제1호A Fubini theorem for generalized analytic Feynman integral on function space이일용, 장승준, 최재길대한수학회 · 대한수학회보2013 · 제50권 제1호Multiple $L_p$ analytic generalized Fourier-Feynman transform onthe Banach algebra장승준, 최재길대한수학회 · 대한수학회논문집2004 · 제19권 제1호A translation theorem for the generalized Fourier--Feynman transform associated with Gaussian process on function space장승준, 최재길, Ae Young Ko대한수학회 · 대한수학회지2016 · 제53권 제5호Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space : an{L}$_{\text{p}}$ theoryDong Hyun Cho대한수학회 · 대한수학회지2004 · 제41권 제2호Convergence theorems in measures for the operator-valued Feynman integralByung Moo Ahn대한수학회 · 대한수학회논문집2002 · 제17권 제1호
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