Smoothness and time–frequency analysis in Sobolev–Besicovitch spaces of almost periodic functions

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2026-05-01 Epub Date: 2025-11-25 DOI:10.1016/j.jat.2025.106255

Juan Miguel Medina , Hernán D. Centeno , Raúl F. Florentín , Mónica Miralles

引用次数: 0

Abstract

Here, smoothness analysis of almost periodic functions is studied. Analogously to the case of

L^{2} (R)

, the smoothness of the class of Besicovitch almost periodic functions is measured in a classic form by controlling, in some sense, the increments

f (x + h) - f (x)

and in a dual form by the decay of its Fourier–Bohr transform or by its approximation properties. The same problem is also treated considering the time–frequency representation given by the Gabor transform. Some results are given as equivalence of norms between appropriate function spaces.

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概周期函数Sobolev-Besicovitch空间的平滑性和时频分析

本文主要研究概周期函数的光滑性分析。与L2(R)的情况类似，Besicovitch类几乎周期函数的平滑性在某种意义上通过控制f(x+h)−f(x)的增量以经典形式测量，并通过其傅里叶-玻尔变换的衰减或其近似性质以对偶形式测量。同样的问题也考虑了由Gabor变换给出的时频表示。给出了适当函数空间间范数等价的一些结果。

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.