论穆西拉克-奥利兹空间中有理函数的逼近

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2024-07-26 DOI:10.1016/j.jat.2024.106083

Wojciech M. Kozlowski , Gianluca Vinti

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引用次数: 0

摘要

我们考虑的是在单位区间上的实值可测函数的 Musielak-Orlicz 空间中，用有理函数进行最佳逼近，并配备 Lebesgue 度量。我们证明了相应多值投影算子的几个性质，包括其半连续性。我们的结果概括了已知的 Lebesgue 和可变 Lebesgues 空间的结果，并可应用于特殊情况，包括 Orlicz 空间和有权重的可变 Lebesgue 空间。我们还谈到了在图像处理中的应用。

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On approximation by rational functions in Musielak–Orlicz spaces

We consider best approximation by rational functions in Musielak–Orlicz spaces of real-valued measurable functions over the unit interval equipped with the Lebesgue measure. We prove several properties of the respective multi-value projection operator, including its semi-continuity. Our results generalise known results for Lebesgue and variable Lebesgues spaces, and can be applied to special cases including Orlicz spaces and variable Lebesgue spaces with weights. We touch upon applications to image processing.

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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.