• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.49-59
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• 2001

In this paper we introduce the modified conditional Yeh-Wiener integral. To do so, we first treat the modified Yeh-Wiener integral. And then we obtain the simple formula for the modified conditional Yeh-Wiener integral and valuate the modified conditional Yeh-Wiener integral for certain functional using the simple formula obtained. Here we consider the functional using the simple formula obtained. Here we consider the functional on a set of continuous functions which are defined on various regions, for example, triangular, parabolic and circular regions.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.627-635
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• 2001

In this paper, we first introduce the modified Yeh-Wiener integral and then consider the modified conditional Yeh-Wiener integral. Here we use the space of continuous functions on a different region which was discussed before. We also evaluate some modified conditional Yeh-Wiener integral with examples using the simple formula for the modified conditional Yeh-Wiener integral.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.75-88
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• 2006

Wiener measure and Wiener measurability behave badly under the change of scale transformation. We express the analytic Feynman integral over $C_0(B)$ as a limit of Wiener integrals over $C_0(B)$ and establish change of scale formulas for Wiener integrals over $C_0(B)$ for some functionals.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.249-260
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• 2014

Cameron and Storvick discovered a change of scale formula for Wiener integral of functionals in a Banach algebra $\mathcal{S}$ on classical Wiener space. We express the analytic Feynman integral of cylinder function as a limit of Wiener integrals. Moreover we obtain the same change of scale formula as Cameron and Storvick's result for Wiener integral of cylinder function. Our result cover a restricted version of the change of scale formula by Kim.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.967-990
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• 2006

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.6
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• pp.8-14
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• 1998

The derivation of the dual integral equation in the spectral domain, which has total fields of the interfaces as unknowns, is investigated. It is analytically shown that the derivation of the dual integral equation is equivalent to deriving the Helmholtz-Kirchhoff integral equation from the Wiener-Hopf integral equation.

• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.91-109
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• 2007

In this paper, we derive a change of scale formula for conditional Wiener integrals, as integral transforms, of possibly unbounded functions over Wiener paths in abstract Wiener space. In fact, we derive the change of scale formula for the product of the functions in a Banach algebra which is equivalent to both the Fresnel class and the space of measures of bounded variation over a real separable Hilbert space, and the $L_p-type$cylinder functions over Wiener paths in abstract Wiener space. As an application of the result, we obtain a change of scale formula for the conditional analytic Fourier-Feynman transform of the product of the functions.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.643-660
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• 2004

In this paper, we give a new formula between the conditional Wiener integral E(F｜X), the conditional Wiener integral of F given X, and the integral with respect to a measure-valued measure, a kind of Bartle integral. Using this formula, we give some examples of evaluation of E(F｜X).

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.811-815
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• 1998

In this paper we define a sample path-valued conditional Yeh-Wiener integral for function F of the type E[F(x)$\mid$x(*,(equation omitted))=$\psi({\blacktriangle})]$, where $\psi$ is in C[0, (equation omitted)] and ${\blacktriangle}$ = (equation omitted) and evaluate a sample path-valued conditional Yeh-Wiener integral using the result obtained.