• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.313-319
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• 2009

In the present paper, a theorem dealing with local property of ${\mid}\;\overline{N},p_n,{\theta}_n\;{\mid}_k$ summability of factored Fourier series which generalizes a result of Mazhar [8], has been proved. Some new results have also been obtained.

• 대한수학회지
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• 제32권4호
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• pp.785-802
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• 1995

It is well known that every periodic function $f \in L^p([0,2\pi]), p > 1$, can be represented by a convergent trigonometric series called the Fourier series of f. Uniqueness of the representing series is very important, and we know that the Fourier series of a periodic function $f \in L^p([0,2\pi])$ is unique.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.377-381
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• 2005

We present a convenient recursive formula for the sums of alternating harmonic series of odd order. The recursion is obtained by expanding in Fourier series certain elementary functions.

• 한국수학사학회지
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• 제26권2_3호
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• pp.163-176
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• 2013

본 논문은 저자의 선행 연구 결과에 따른 부가적인 연구로 '푸리에 급수의 $\mathfrak{L}^1$-수렴성'에 관한 많은 업적을 남긴 세계적인 수학자인 스타노제빅(Caslav V. Stanojevic)을 중심으로 20세기 후반부터 21세기 초까지(1973-2002) 30년간 그의 연구결과를 순차적으로 고찰하여 푸리에 급수의 $\mathfrak{L}^1$-수렴성 연구자들의 2012년까지 소 계보를 조사한다.

• 대한수학회보
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• 제54권3호
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• pp.935-952
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• 2017

It is natural to try to find a kernel such that its convolution of integrable functions converges faster than that of the $Fej{\acute{e}}r$ kernel. In this paper, we introduce a weighted Fourier partial sums which are written as the convolution of signed good kernels and prove that the weighted Fourier partial sum converges in $L^2$ much faster than that of the $Ces{\grave{a}}ro$ means. In addition, we present two numerical experiments.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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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.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.955-969
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• 2003

The classical Fourier analysis, which is the typical frequency domain approach, is used to detect periodic trends that are of the sinusoidal shape in time series data. In this article, using a sequence of periodic step functions, describes an adaptive Fourier series where the patterns may take general periodic shapes that include sinusoidal as a special case. The results, which extend both Fourier analysis and Walsh-Fourier analysis, are applies to investigate the shape of the periodic component. Through the real data, compare the goodness-of-fit of the model using two methods, the adaptive Fourier method which is proposed method in this paper and classical Fourier method.

• 대한수학회보
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• 제55권1호
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• pp.107-114
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• 2018

In this paper, we give some identities for the higher-order Euler functions arising from the Fourier series of them. In addition, we investigate some formulae related to Bernoulli functions which are derived from our identities.

• East Asian mathematical journal
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• 제35권3호
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• pp.297-303
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• 2019

In this paper, the author introduces the class $L^p$-BV of functions which are of bounded variation in the sense of $L^p$-norm and investigates the degree of convergence for Fourier series of functions belonging to this class.

• East Asian mathematical journal
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• 제37권3호
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• pp.289-293
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• 2021

In this paper, we investigate the degree of approximation of a function f belonging to the generalized Zygmund class Zyg^ω(α, γ) by Cesaro means of its Fourier series.