Best approximations and their extensions in Lorentz Gamma spaces

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2025-07-08 DOI:10.1016/j.jat.2025.106212

F.D. Kovac , F.E. Levis , L. Zabala

引用次数: 0

Abstract

In this article, we investigate the best approximation operator from a finite-dimensional linear space defined on Lorentz Gamma spaces

Γ_{w, p}

for

1 \leq p < \infty

. We extend the best approximation operator from

Γ_{w, p}

to the larger space

Γ_{w, p - 1}

and establish several key properties of these operators.

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洛伦兹空间中的最佳逼近及其扩展

在本文中，我们研究了在Lorentz Gamma空间Γw上定义的有限维线性空间中的最佳逼近算子，p为1≤p<；∞。我们将最佳逼近算子从Γw，p推广到更大的空间Γw，p−1，并建立了这些算子的几个关键性质。

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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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.