• 한국수학사학회지
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• 제27권1호
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• pp.81-93
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• 2014

The $L^1$-convergence of Fourier series problems through additional assumptions for Fourier coefficients were presented by W. H. Young in 1913. We say that they are the classical results. Using modified trigonometric series is the convenience method to study the $L^1$-convergence of Fourier series problems. they are called the neoclassical results. This study concerns with the $L^1$-convergence of Fourier series. We introduce the classical and neoclassical results of $L^1$-convergence sequentially. In particular, we investigate $L^1$-convergence results focused on the results of Bhatia's studies. In conclusion, we present the research minor lineage of Bhatia's studies and compare the classes of $L^1$-convergence mutually.

• 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.

• 통합자연과학논문집
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• 제1권3호
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• pp.216-220
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• 2008

In general the Banach space $L^1(T^1)$ doesn't admit convergence in norm. Thus the convergence in norm of the partial sums can not be characterized in terms of Fourier coefficients without additional assumptions about the sequence$\{^{\^}f(\xi)\}$. The problem of $L^1(T^1)$-convergence consists of finding the properties of Fourier coefficients such that the necessary and sufficient condition for (1.2) and (1.3). This paper showed that let $\{{\alpha}_{\kappa}\}{\in}BV$ and ${\xi}{\Delta}a_{\xi}=o(1),\;{\xi}{\rightarrow}{\infty}$. Then (1.1) is a Fourier series if and only if $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.31-41
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• 2014

In this paper criterion for $L_1$-convergence of a certain cosine sums with quasi hyper-convex coefficients is obtained.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.323-328
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• 2007

In this paper, we extend the result of Ram [3] and also study the $L^1$-convergence of the $r^{th}$ derivative of cosine series.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권1호
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• pp.59-64
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• 2009

In this paper, we study the relations between L-fuzzy topologies and L-filters on a strictly two-sided, commutative quantale lattice L. We define an L-fuzzy neighborhood filter and introduce the notion of L-filter convergence in L-fuzzy topological spaces.

• Journal of the Korean Data and Information Science Society
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• 제3권1호
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• pp.25-31
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• 1992

Some results relating to $C_{0}(R)\;and\;L^{1}(R)$ spaces with application to kernel density estimators will be introduced. First, random elements in $C_{0}(R)\;and\;L^{1}(R)$ are discussed. Then, complete convergence limit theorems are given to show that these results can be used in establishing uniformly consistency and $L^{1}$ consistency.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.73-85
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• 2005

In this paper a criterion for $L^1-convergence$ of a new modified sine sums is obtained by using $Ces{\grave{a}}ro$ means of integral and non-integral orders.

• 한국수학사학회지
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• 제22권1호
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• pp.25-40
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• 2009

본 논문에서는 푸리에의 생애와 18세기 말 그의 스승과 19세기부터 20세기까지는 그의 제자와 후학들의 소계보를 살펴보고 특히, 비교적 덜 접근된 러시아 수학자들의 푸리에 급수의 $L^1$-수렴성에 대한 연구결과들 중 푸리에 계수 성질을 이용한 푸리에 급수 수렴성에 대해 매우 의미 있는 연구를 이룩한 콜모고로프, 테라코브스키의 연구결과에 관심을 갖고 이들의 연구 결과를 비교하여 조사하였다.

• 한국환경과학회지
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• 제31권7호
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• pp.569-577
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• 2022

This study aimed to evaluate the growth of Cichorium intybus, Brassica juncea, and Lactuca sativa at varying seed ratios, and to suggest an efficient management plan for sustainable indoor agriculture systems. It was treated with mixed sowing as follows: 30 chicory seeds (chicory alone: CC), 22 chicory seeds + 8 lettuce seeds (C₃L₁), 20 chicory seeds + 10 lettuce seeds (C₂L₁), 15 chicory seeds + 15 lettuce seeds (C₁L₁) as intraspecies, and 30 mustard seeds (mustard alone: MC), 22 mustard seeds + 8 lettuce seeds (M₃L₁), 20 mustard seeds + 10 lettuce seeds (M₂L₁), 15 mustard seeds + 15 lettuce seeds (M₁L₁) as interspecies. The study identified the competitive response in seed germination between Cichorium intybus and Lactuca sativa, and in the C₃L₁ experimental group, Lactuca sativa had the highest leaf length, root length, chlorophyll content, and fresh weight. Therefore, the higher the ratio of Cichorium intybus, the higher the growth and productivity of Lactuca sativa; however, higher the ratio of Lactuca sativa, the lower the growth of Cichorium intybus. Furthermore, the nitrogen and potassium content in the substrate was the highest in the C₃L₁ experimental grorp which had the highest seeding rate of the Cichorium intybus. Comparing the groups Brassica juncea and Lactuca sativa, the higher the seeding ratio of Lactuca sativa, the higher the growth and productivity of Brassica juncea. Therefore, a companion seeding of Brassica juncea and Lactuca sativa is beneficial; this could be effective in having a high seeding ratio of Lactuca sativa.