单侧科洛夫金近似

IF 0.9 3区数学 Q2 MATHEMATICS Journal of Approximation Theory Pub Date : 2024-01-03 DOI:10.1016/j.jat.2023.106011

Michele Campiti

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引用次数: 0

摘要

在本文中，我们详细研究了科洛夫金闭包的一些特征，还引入了单面上科洛夫金闭包和单面下科洛夫金闭包的概念。我们提供了这些新闭包的一些完整特征，它们区分了近似函数在科洛夫金系统中的作用。我们还介绍了可积分函数空间中经典科洛夫金闭合的一些新特征。同样，我们可以引入并描述上科罗夫金闭包和下科罗夫金闭包。最后，我们将举例说明这些新闭包的意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Onesided Korovkin approximation

In this paper we study in detail some characterizations of Korovkin closures and we also introduce the notions of onesided upper and lower Korovkin closures. We provide some complete characterizations of these new closures which separate the roles of approximating functions in a Korovkin system. We also present some new characterizations of the classical Korovkin closure in spaces of integrable functions. Again we can introduce and characterize the upper and lower Korovkin closures. Finally, we provide some examples which justify the interest in these new closures.

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.

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