Wavelet characterization of exponentially weighted Besov space with dominating mixed smoothness and its application to function approximation

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2024-03-11 DOI:10.1016/j.jat.2024.106037

Yoshihiro Kogure, Ken’ichiro Tanaka

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引用次数: 0

Abstract

Although numerous studies have focused on normal Besov spaces, limited studies have been conducted on exponentially weighted Besov spaces. Therefore, we define exponentially weighted Besov space $V B_{p, q}^{δ, w} (R^{d})$ whose smoothness includes normal Besov spaces, Besov spaces with dominating mixed smoothness, and their interpolation. Furthermore, we obtain wavelet characterization of $V B_{p, q}^{δ, w} (R^{d})$ . Next, approximation formulas such as sparse grids are derived using the determined formula. The results of this study are expected to provide considerable insight into the application of exponentially weighted Besov spaces with mixed smoothness.

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具有支配性混合平滑的指数加权贝索夫空间的小波特征及其在函数逼近中的应用

虽然大量研究都集中在正态贝索夫空间，但对指数加权贝索夫空间的研究还很有限。因此，我们定义了指数加权贝索夫空间，其平滑度包括正常贝索夫空间、具有支配性混合平滑度的贝索夫空间及其插值。此外，我们还获得了贝索夫空间的小波特征。接下来，我们将利用确定的公式推导出稀疏网格等近似公式。本研究的结果有望为具有混合平滑性的指数加权贝索夫空间的应用提供可观的启示。

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.