Pointwise strong approximation of almost periodic functions
Rados{\l}awa Kranz, W{\l}odzimierz {\L}enski, Bogdan Szal
TL;DR
This paper investigates how well almost periodic functions can be approximated pointwise using matrix means of their Fourier series, providing new insights into their strong approximation properties.
Contribution
It introduces a novel approach to pointwise approximation of almost periodic functions within the GM(2b) class using matrix means of Fourier partial sums.
Findings
Established bounds for deviations in strong mean
Extended approximation results to the GM(2b) class
Provided new estimates for Fourier series partial sums
Abstract
We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Mathematical Approximation and Integration · Advanced Harmonic Analysis Research