1991
DOI: 10.2307/2048743
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Conditional Analytic Feynman Integrals on Abstract Wiener Spaces

Abstract: Abstract.In this paper we define the concept of a conditional analytic Feynman integral of a function F on an abstract Wiener space B given a function X and then establish the existence of the conditional Feynman integral for all functions in the Fresnel class on B . We also use the conditional Feynman integral to provide a fundamental solution to the Schrödinger equation.

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Cited by 2 publications
(2 citation statements)
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“…In [14], Chung and Skoug introduced the concept of a conditional Feynman integral and applied their results to obtain a fundamental solution of Schrödinger equation, whereas in [18], Park and Skoug introduced the concept of a conditional Fourier-Feynman transform on Wiener space. Other work involving conditional Feynman integrals and conditional Fourier-Feynman transforms on Wiener space include [3,13]. In [8], Chang, Choi and Skoug established various integration by parts formulas for conditional generalized Feynman integrals and conditional generalized Fourier-Feynman transforms(CGFFT) using the conditioning function X(x) = x(T ), x ∈ C a,b [0, T ].…”
Section: Introductionmentioning
confidence: 99%
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“…In [14], Chung and Skoug introduced the concept of a conditional Feynman integral and applied their results to obtain a fundamental solution of Schrödinger equation, whereas in [18], Park and Skoug introduced the concept of a conditional Fourier-Feynman transform on Wiener space. Other work involving conditional Feynman integrals and conditional Fourier-Feynman transforms on Wiener space include [3,13]. In [8], Chang, Choi and Skoug established various integration by parts formulas for conditional generalized Feynman integrals and conditional generalized Fourier-Feynman transforms(CGFFT) using the conditioning function X(x) = x(T ), x ∈ C a,b [0, T ].…”
Section: Introductionmentioning
confidence: 99%
“…The Wiener process used in [3,13,14,17,18,21] is stationary in time and is free of drift while the stochastic process used in [2, 4, 7-10, 11, 19] and in this paper is nonstationary in time and is subject to a drift a(t). However when a(t) ≡ 0 and…”
Section: Introductionmentioning
confidence: 99%