Sobolev空间中平移不变子空间的同时密度阶

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2025-02-06 DOI:10.1016/j.jat.2025.106147

Ch. Boukeffous , A. San Antolín

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引用次数: 0

摘要

Zhao（1995）在Sobolev空间中的移不变子空间中引入了同时逼近阶（m,k）的概念。此外，还证明了同时提供近似阶（m,k）的主移不变子空间的一个性质。在这篇笔记中，我们证明了另一个用平移不变子空间的一些适当的扩展线性映射展开的表征。此外，我们引入了同时密度阶（m,k）的概念，并给出了平移不变子空间具有期望同时密度的充分必要条件。为了给出我们的条件，我们将解释平移不变子空间的产生子的傅里叶变换在原点的邻域上的行为。为此，我们将使用经典的近似连续性概念。

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On simultaneous density order from shift invariant subspaces in Sobolev spaces

The notion of simultaneous approximation order

(m, k)

from shift-invariant subspaces in Sobolev spaces was introduced in the paper by Zhao (1995). Moreover, a characterization of those principal shift-invariant subspaces that provide simultaneous approximation order

(m, k)

was proved there. In this note, we prove another characterization using dilated by some adequate expansive linear maps of a shift-invariant subspace. In addition, we introduce the notion of simultaneous density order

(m, k)

and give necessary and sufficient conditions on a shift-invariant subspace to have a simultaneous density desired. To give our conditions, we shall explain the behavior on a neighborhood of the origin of the Fourier transform of the generators of a shift-invariant subspace. For this, we will use the classical notion of approximate continuity.

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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.