논문KCI 등재
Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wiener space : an{L}$_{\text{p}}$ theory
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Abstract
In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier- Feynman transforms. Also, we evaluate the conditional Fourier- Feynman transforms of the functions of the forms exp T 0 θ(s, x(s))ds, exp T 0 θ(s, x(s))dsφ(x(T)), exp T 0 θ(s, x(s))dζ(s), exp T 0 θ(s, x(s))dζ(s)φ(x(T)) which are of interest in Feynman integration theories and quantum mechanics.
참고문헌 (15)
- "Some Banach algebras of analytic Feynmanintegrable functionals", Springer-Verlag
- "Conditional Fourier-Feynman transform and convolution product over Wiener paths in abstract Wienerspace", 14(3), pp.217~235 (2003)
- "A conditional anlytic Feynmanintegral over Wiener paths"
- "Convolution and analytic Fourier-Feynman transforms over paths in abstract Wiener space", 13, pp.345~362 (2002)
- "The eect of drift on conditional Fourier-Feynmantransforms and conditional convolution products", 2(4), pp.505~527 (2000)
- "Generalized Feynman integrals using analyticcontinuation in several complex variables" (1984)
- "The law of the iterated logarithm for Brownian motionin a Banach space" (1973)
- "Gaussian measures in Banach spaces Lecture Notes in Math. 463" (1975), Springer-Verlag
- "A simple formula for conditional Wiener integrals withapplications" (1988)
- "Conditional Fourier-Feynman transforms and conditional convolutionproducts", 38(1), pp.61~76 (2001)
- "The Wiener integral over paths in abstract Wiener space" (1992)
- "Introduction to Fourier analysis on Euclidean spaces" (1971), Princeton Univ. Press
- "Inversion of conditional expectations" (1974)
- "Inversion of conditional Wiener integrals" (1975)
- "The analytic Feynman integral over paths in abstract Wiener space", 10(1), pp.93~107 (1995)
관련 논문AI추천
Conditional Fourier-Feynman transforms of variations over Wiener paths in abstract Wiener space조동현대한수학회 · 대한수학회지2006 · 제43권 제5호Conditional generalized Fourier-Feynman transform and conditional convolution product on a Banach algebra장승준, 최재길대한수학회 · 대한수학회보2004 · 제41권 제1호Conditional Fourier-Feynman transform and conditional convolution product associated with vector-valued conditioning function고애영, 최재길한국수학교육학회 · 이론수학과 교직수학2023 · 제30권 제2호CONDITIONAL FOURIER–FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION심상길, 최재길대한수학회 · 대한수학회보2023 · 제60권 제5호Conditional Fourier-Feynman transforms and convolutions of unbounded functions on a generalized Wiener space조동현대한수학회 · 대한수학회지2013 · 제50권 제5호Transforms and convolutions on function space장승준, 최재길대한수학회 · 대한수학회논문집2009 · 제24권 제3호
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