• 충청수학회지
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• 제27권2호
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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.

• 대한수학회지
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• 제43권5호
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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.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.587-600
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• 2016

We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.

• 대한수학회보
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• 제50권6호
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• pp.1973-1979
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• 2013

The main purpose of this paper is to give the Wintner theorem in unital complete random normed algebras which is a random generalization of the classical Wintner theorem in Banach algebras. As an application of the Wintner theorem in unital complete random normed algebras, we also obtain that the identity operator on a complete random normed module is not a commutator.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.335-348
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• 2008

We define Fourier-Yeh-Feynman transform and convolution product on the Yeh-Wiener space, and establish the existence of Fourier-Yeh-Feynman transform and convolution product for functionals in a Banach algebra $\mathcal{S}(Q)$. Also we obtain Parseval's relation for those functionals.

• 호남수학학술지
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• 제33권2호
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• pp.207-221
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• 2011

We examine the various relationships that exist among the Fourier-Yeh-Feynman transform, convolution and the first variation for functionals on Yeh-Wiener space that belong to a Banach algebra S(Q).

• 대한수학회보
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• 제57권1호
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• pp.31-35
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• 2020

With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in [2] that if n ∈ {3, 4} is fixed, A, B are commutative algebras and h : A → B is an n-Jordan homomorphism, then h is an n-ring homomorphism. In this paper, we extend this result for all n ≥ 3.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.389-401
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• 2015

We will show the general solution of the functional equation f(x + ay) + f(x − ay) + 2(a² − 1)f(x) = a²f(x + y) + a²f(x − y) + 2a²(a² − 1)f(y) and investigate the stability of quartic Lie *-derivations associated with the given functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• 대한수학회논문집
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• 제11권1호
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• pp.175-190
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• 1996

In this paper we establish the existence of the conditional Feynman integral of certain functions which are not in the Banach algebra S of functions on Wiener space which are a kind of stochastic Fourier transform of complex Borel measures on $L^2[a, b]$. This result is used to provide the fundamental solution for the Schr$\ddot{o}$dinger equation for the forced harmonic potential.