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Convergence rate of hybrid sampling series associated with wavelets
심홍태,Joongsung Kwon 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.14 No.-
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.
Jump discontinuity in two dimensions
심홍태,Chin-Hong Park 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
The concept of Gibbs’ phenomenon has not been made for higherdimension in wavelets. In this paper we extend the concept in two dimensionalwavelets. We give the fundamental concept of jump discontinuity in two dimen-sions. We provide the criteria for the existence of Gibbs phenomenon for bothseparable and tensor product wavelets.
Periodic wavelet on interval by regular wavelets
심홍태,Chin-Hong Park 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
Multiresoluton analysis(MRAof space of square integrable func-tions dened on whole entire line has been well-known. But for many applica-tions, MRA on bounded interval was required and studied. In this paper we givea MRA for L2(0,1) by means of periodic wavelets based on regular MRA forL2(R) and give the convergence of partial sums.
Convergence rate of convolution type delta sequence in higher dimension
심홍태,Chin-Hong Park 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2
Delta sequences play an important role in convergence and approximation theory. Much of classical approximation theory is based on delta sequence. The rate of convergence of certain types of these sequences in Sobolev spaces has recently been studied. Here we estimate convergence rate of convolution type delta sequence in higher dimension.
Gibbs Phenomenon for trigonometric interpolation
심홍태,Chin-Hong Park 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
The Gibbs’ phenomenon for the classical Fourier series is known.This occurs for almost all series expansions. This phenomenon has been observedeven in sampling series.In this paper, we show the existence of Gibbs phenomenonfor trigonometric interpolating polynomial by a simple and dierent manner fromthe wok[4].
ON FUNCTIONS DEFINED BY ITS FOURIER TRANSFORM
심홍태,권중성 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
Fourier transform is well known for trigonometric systems. It is also a very useful tool for the construction of wavelets. The method of constructing wavelets has evolved as times went by. We review some methods. Then we do some calculations on wavelets defined by its Fourier transform.
Remarks on kernel for Wavelet expansions in multidimensions
심홍태,Joong-Sung Kwon 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.
Approximation by convolution type delta sequence in higher dimension
심홍태,Chin-Hong Park 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
In this paper we deal with functions in higher dimension. We pro-vide several convergence theorem for approximation by convolution type deltasequence. We also give sucient and necessary condition for Gibbs phenomenonto exist.
Survey of Gibbs phenomenon from Fourier series to hybrid sampling series
심홍태,Chin-Hong Park 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2
An understanding of Fourier series and their generalization is important for physics and engineering students, as much for mathematical and physical insight as for applications. Students are usually confused by the so-called Gibbs’ phenomenon, an overshoot between a discontinuous function and its approximation by a Fourier series as the number of terms in the series becomes indefinitely large. In this paper we give short story of Gibbs phenomenon in chronological order.
A regularity summability and its application to wavelet expansions
심홍태 선문대학교 자연과학대학 2000 자연과학논총 Vol.3 No.-
레글러 합을 정의하고 이를 웨이브릿 전개에 적용한다. 그리하여 웨이브릿 전개에서의 레귤러 합의 수렴속도를 조사하고, 함수들의 유사양함수의 수열이 레글러 합에 의해서도 유사양함수 열이 됨을 보인다. We define a regular summability and apply it to orthogonal wavelet expansions. Then we investigate the rate of convergence for regular summability in wavelet expansions. We also show that regular summability of quasi-positive delta sequence of functions becomes quasi-postive.