• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.117-124
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• 2012

In this paper, we present some remarks on the correlations between s and w domains when a discrete-time transfer function is converted from z-plane by using the w-transform. With time response specifications, when a digital filter or controller is designed in z-plane, the w-transform is useful for the purpose if only the w-transformed system closely approximates to the continuous-time system. It will be shown that the approximation is accomplished only in the specific region depending on sampling time. Also, it is noted that such an approximation should be carefully dealt with for the case where a discrete-time reference transfer function is synthesized for the use of direct digital design.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.649-671
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• 2020

In this paper we give the harmonic analysis associated with the Cherednik operators, next we define and study the Cherednik wavelets and the Cherednik windowed transforms on ℝd, in the W-invariant case, and we prove for these transforms Plancherel and inversion formulas. As application we give these results for the Gaussian Cherednik wavelets and the Gaussian Cherednik windowed transform on ℝd in the W-invariant case.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.694-696
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• 2001

인터넷상에서 메시지 교환을 위하여 XML의 사용이 급증함에 따라 XML문서의 보안이 필요하게 되었고, 이에 W3C는 XML-Signature 표준안을 제안 하고 있다. XML-Signature 표준 스펙에서는 서명할 문서의 내용을 선택 하는 방법으로 Transform 알고리즘들을 제안하고 있고, 그 알고리즘들은 서명자가 원하는 문서의 일부분만을 선택하거나, 변형하는 방법들을 기술하고 있다. 서명 시스템은 그런 Transform 알고리즘을 사용하여 문서의 전체 흑은 원하는 부분만을 선택하여 서명 함으로써 서명의 생성 및 검증의 처리속도를 높일 수 있고, 송.수신 시 효율을 높일 수 있고, 기존의 문서를 재사용 할 수 있는 등의 장점을 제공 하고 있다. 본 논문에서는 위와 같은 처리를 할 수 있는 4가지 Transform 알고리즘(XPath, XSLT, Enveloped. Base64 Transform)과 XML문서들의 무결성을 유지하기 위해 W3C의 Canonical XML 스펙을 기반으로 하는 Canonicalization Transform 알고리즘을 설계, 구현하였다. 이 Transform 알고리즘들은 XML 디지틸 서명 뿐 만 아니라 문서를 선택적으로 변환하는 응용등에서 사용할 수 있다.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.4
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• pp.1-5
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• 1976

Spectrum의 시간기복을 나타내는 시간 및 주파수의 함수 F(w,t,T) 및 W(w,t,T)를 정의하였고, 실례에 적용시켰다. Fourier변환을 f(t)와 Phasor ejwt와의 Correlation으로 정의하였고 그 변환시분이 시간마다의 성분의 합계이어서 t 시각에서의 Spectrum을 그 근거에서의 f(t)값에만 의함을 증명하였다. Two new time functions defining Time Dependent Fourier Transform F(w,t,T) and Time Dependent Spectrum Density W(w,t,T) are deduced. courier transform is defined as the correlation between the time function f(t) and phasor ejwt. Several theorems corncerning the new functions are proved in order to verify the instantaneous cause a effet of the function f(t) and the nuctuating spectrum.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.221-267
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• 2019

In the five first sections of this paper we define and study the hypergeometric transmutation operators $V^W_k$ and $^tV^W_k$ called also the trigonometric Dunkl intertwining operator and its dual corresponding to the Heckman-Opdam's theory on ${\mathbb{R}}^d$. By using these operators we define the hypergeometric translation operator ${\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, and its dual $^t{\mathcal{T}}^W_x$, $x{\in}{\mathbb{R}}^d$, we express them in terms of the hypergeometric Fourier transform ${\mathcal{H}}^W$, we give their properties and we deduce simple proofs of the Plancherel formula and the Plancherel theorem for the transform ${\mathcal{H}}^W$. We study also the hypergeometric convolution product on W-invariant $L^p_{\mathcal{A}k}$-spaces, and we obtain some interesting results. In the sixth section we consider a some root system of type $BC_d$ (see [17]) of whom the corresponding hypergeometric translation operator is a positive integral operator. By using this positivity we improve the results of the previous sections and we prove others more general results.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.779-787
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• 2017

Let m be the Lebesgue measure on ${\mathbb{C}}$ normalized to $m(D)=1,{\mu}$ be an invariant measure on D defined by $d_{\mu}(z)=(1-{\mid}z{\mid}^2)^{-2}dm(z)$. For $f{\in}L^1(D^n,m{\times}{\cdots}{\times}m)$, Bf the Berezin transform of f is defined by, $$(Bf)(z_1,{\ldots},z_n)={\displaystyle\smashmargin{2}{\int\nolimits_D}{\cdots}{\int\nolimits_D}}f({\varphi}_{z_1}(x_1),{\ldots},{\varphi}_{z_n}(x_n))dm(x_1){\cdots}dm(x_n)$$. We prove that if $f{\in}L^1(D^2,{\mu}{\times}{\mu})$ is radial and satisfies ${\int}{\int_{D^2}}fd{\mu}{\times}d{\mu}=0$, then for every bounded radial function ${\ell}$ on $D^2$ we have $$\lim_{n{\rightarrow}{\infty}}{\displaystyle\smashmargin{2}{\int\int\nolimits_{D^2}}}(B^nf)(z,w){\ell}(z,w)d{\mu}(z)d{\mu}(w)=0$$. Then, using the above property we prove n-harmonicity of bounded function which is invariant under the Berezin transform. And we show the same results for the weighted the Berezin transform in the polydisc.

• Journal of Electrical Engineering and information Science
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• v.1 no.2
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• pp.125-133
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• 1996

In this paper, we dicuss on the properties related to the circular filtering in orthogonal transform domain. The efficient filtering schemes in six orthogonal transform domains are presented by generalizing the convolution-multiplication property of the DFT. In brief, the circular filtering can be accomplished by multiplying the transform domain filtering matrix W, which is shown to be very sparse, yielding the computational gains compared with the time domain processing. As an application, decimation and interpolation techniques in orthogonal transform domains are also investigated.

• Proceedings of the Optical Society of Korea Conference
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• 1996.09a
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• pp.50-50
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• 1996

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.119-142
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• 2021

In this paper, we first introduce a new L_p analytic Fourier-Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L_p-AFFTSB, the convolution product, and the gradient operator for several types of functionals.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.137-160
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• 2006

We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.