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On approximation by rational functions in Musielak–Orlicz spaces 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 Pub Date : 2024-07-26 DOI: 10.1016/j.jat.2024.106083
Wojciech M. Kozlowski , Gianluca Vinti

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.

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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引用次数: 0
The Machado–Bishop theorem in the uniform topology 统一拓扑中的马查多-毕夏普定理
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-26 DOI: 10.1016/j.jat.2024.106085
Deliang Chen

The Machado–Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado’s distance formula for bounded weighted vector-valued functions. A number of applications are given; in particular, some types of the Bishop–Stone–Weierstrass theorem for bounded vector-valued continuous spaces in the uniform topology are discussed; the splitting of C(I×J,XY) as the closure of C(I,X)C(J,Y) in different senses and the extension of continuous vector-valued functions are studied.

对于在无穷大处消失的加权矢量值函数,马查多-毕夏普定理已被广泛研究。本文给出了有界加权向量值函数的马查多距离公式。本文给出了一些应用;特别是讨论了均匀拓扑中有界向量值连续空间的 Bishop-Stone-Weierstrass 定理的一些类型;研究了作为 C(I,X)⊗C(J,Y) 闭包的 C(I×J,X⊗Y) 在不同意义上的分裂以及连续向量值函数的扩展。
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引用次数: 0
Remembering Peter Benjamin Borwein (May 10, 1953–August 23, 2020) 缅怀彼得-本杰明-博文(1953 年 5 月 10 日-2020 年 8 月 23 日)
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-06 DOI: 10.1016/j.jat.2024.106070
Tamás Erdélyi
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引用次数: 0
Peter Borwein: A philosopher’s mathematician 彼得-博文哲学家的数学家
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106071
David H. Bailey
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引用次数: 0
In memory of Peter Borwein 纪念彼得-博尔文
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106072
Stephen Choi
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引用次数: 0
In memory of Peter Borwein 纪念彼得-博尔文
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106075
Boris Shekhtman
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引用次数: 0
Remembering Peter Benjamin Borwein (May 10, 1953–August 23, 2020) 缅怀彼得-本杰明-博文(1953 年 5 月 10 日 - 2020 年 8 月 23 日)
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106073
Doron S. Lubinsky
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引用次数: 0
PII: S0021-9045(24)00055-8
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106069
Paul Nevai, Amos Ron
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引用次数: 0
In Memoriam: Peter Benjamin Borwein (1953–2020) 悼念:彼得-本杰明-博文(1953-2020)
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-07-05 DOI: 10.1016/j.jat.2024.106074
Michael J. Mossinghoff

Peter Borwein had wide-ranging mathematical interests, and was a pioneer in computational and experimental investigations in many areas. We fondly recall some of his interests and contributions in a number of topics in analysis, number theory, and other areas, especially work where computation and experimentation played an important role. This includes his work on a number of extremal problems regarding Littlewood polynomials and other families of integer polynomials with restricted coefficients, questions regarding the Mahler measure of an integer polynomial, problems on merit factors and Barker sequences, the Prouhet–Tarry–Escott problem, problems of Pólya and Turán regarding sums of the Liouville function, and questions in combinatorial geometry regarding arrangements of points and lines.

彼得-博文对数学有着广泛的兴趣,是许多领域计算和实验研究的先驱。我们深情地回忆起他在分析、数论和其他领域的一些课题上的兴趣和贡献,尤其是在计算和实验方面发挥重要作用的工作。这包括他在一些极值问题上的工作,这些问题涉及 Littlewood 多项式和其他具有受限系数的整数多项式族、整数多项式的马勒度量问题、绩因子和巴克序列问题、Prouhet-Tarry-Escott 问题、Pólya 和 Turán 关于 Liouville 函数和的问题,以及组合几何中关于点和线排列的问题。
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引用次数: 0
Corrigendum to “Strong uniqueness and alternation theorems for relative Chebyshev centers” [J. Approx. Theory, 293 (2023) 105917] 对 "相对切比雪夫中心的强唯一性和交替定理 "的更正 [J. Approx.
IF 0.9 3区 数学 Q2 MATHEMATICS Pub Date : 2024-06-26 DOI: 10.1016/j.jat.2024.106067
F.E. Levis , C.V. Ridolfi , L. Zabala

We correct an error in the statement of Levis et al. (2023, Theorem 4.5).

我们纠正了莱维斯等人(2023,定理 4.5)的陈述中的一个错误。
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引用次数: 0
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Journal of Approximation Theory
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