• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.725-738
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• 2005

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.839-857
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• 2010

We give a set of continuous characterizations for the homogeneous Triebel-Lizorkin spaces and use them to study boundedness properties of Fourier multiplier operators whose symbols satisfy a generalization of H$\ddot{o}$rmander's condition. As an application, we give new direct proofs of the imbedding theorems of the Sobolev type.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.61-76
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• 2001

In this paper we define the concept of a conditional Fourier-Feynman transform and a conditional convolution product and obtain several interesting relationships between them. In particular we show that the conditional transform of the conditional convolution product is the product of conditional transforms, and that the conditional convolution product of conditional transforms is the conditional transform of the product of the functionals.

• Honam Mathematical Journal
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• v.33 no.2
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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).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.31-40
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• 2004

In this paper we point out an approximation for the Fourier transform for functions of bounded variation and study the approximation error of certain associated quadrature rules.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.10a
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• pp.300-305
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• 1998

A method of calculating wear amount which is based on digitally measured surface profile was suggested. The original profile of worn out profile was estimated from its adjacent surface profile by using least squares curve fitting with Fourier series. The approximated curve was well fitted to original surface profile. With this approach, more accurate calculation of the wear amount will be possible.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.267-275
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• 2004

While the convergence of the classical Fourier series has been well known, the rate of its convergence is not well acknowledged. The results regarding the rate of convergence of the Fourier series and wavelet expansions can be found in the book of Walter[5]. In this paper, we give the rate of convergence of hybrid sampling series associated with orthogonal wavelets.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.7-16
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• 2001

We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

• Proceedings of the Korean Information Science Society Conference
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• 2000.04b
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• pp.505-507
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• 2000

현재 백혈병 진단에서 사용중인 방법은 골수영상을 획득하고 이를 관찰하여 비정상의 백혈구의 형태, 백혈구 핵의 크기와 추출된 골수에서의 백혈구가 차지하는 비율을 이용하여 진단하고 있다. 비정상적인 모양을 띠고 있는 백혈구의 검출은 백혈병 진단에 있어 중요한 정보로 사용된다. 백혈구의 이상 형태중 다수의 구멍이 있는 백혈구는 검출하기 위해 골수영상에서 백혈구 영역을 추출하고 이에 대해 UNL transform을 이용하여 모양 특징을추출하였다. UNL Fourier transform은 원영상의 이동(translation), 회전(rotation), 확대/축소(scale)에 대해 불변인 성질을 지니므로 이를 이용해 백혈구의 모양 특징을 추출하고 유사도 검색을 통해 비정상의 백혈구를 검출하였다.