Direct and inverse approximation theorems in the Besicovitch-Museilak-Orlicz spaces of almost periodic functions

2021/12/13 by S. O. Chaichenko, Chaichenko, Stanislav, Andrii Shidlich +3
Mathematics · #26A15 #41A17 #41A25 #42A32 #42A75 #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2112.06664

openalex publication_date 2021/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point in infinity and their Orlicz norms are finite. Special attention is paid to the study of cases when the constants in these theorems are unimprovable.

Related

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• Actual problems of the approximation theory in metrics of discrete spaces on sets of summable periodic and almost periodic functions
• Norm Inequalities for the Fourier Coefficients of Some Almost Periodic Functions
• Approximation of functions by linear summation methods in the Orlicz type spaces
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