# Pointwise strong approximation of almost periodic functions

Radosława Kranz; Włodzimierz Łenski; Bogdan Szal

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)

- Volume: 36, Issue: 1, page 45-63
- ISSN: 1509-9407

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topRadosława Kranz, Włodzimierz Łenski, and Bogdan Szal. "Pointwise strong approximation of almost periodic functions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.1 (2016): 45-63. <http://eudml.org/doc/286887>.

@article{RadosławaKranz2016,

abstract = {We consider the class GM(₂β) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.},

author = {Radosława Kranz, Włodzimierz Łenski, Bogdan Szal},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {almost periodic functions; rate of strong approximation; summability of Fourier series; rate of approximation; Lipschitz class},

language = {eng},

number = {1},

pages = {45-63},

title = {Pointwise strong approximation of almost periodic functions},

url = {http://eudml.org/doc/286887},

volume = {36},

year = {2016},

}

TY - JOUR

AU - Radosława Kranz

AU - Włodzimierz Łenski

AU - Bogdan Szal

TI - Pointwise strong approximation of almost periodic functions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2016

VL - 36

IS - 1

SP - 45

EP - 63

AB - We consider the class GM(₂β) in pointwise estimate of the deviations in strong mean of almost periodic functions from matrix means of partial sums of their Fourier series.

LA - eng

KW - almost periodic functions; rate of strong approximation; summability of Fourier series; rate of approximation; Lipschitz class

UR - http://eudml.org/doc/286887

ER -

## References

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- [6] W. Łenski, Pointwise strong and very strong approximation of Fourier series, Acta Math. Hung. 115 (3), 207, 215-233. Zbl1136.41004
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- [8] P. Pych-Taberska, Approximation properties of the partial sums of Fourier series of almost periodic functions, Studia Math. XCVI (1990), 91-103.
- [9] S. Tikhonov, Trigonometric series with general monotone coefficients, J. Math. Anal. Appl. 326 (1) (2007), 721-735. doi: 10.1016/j.jmaa.2006.02.053 Zbl1106.42003
- [10] S. Tikhonov, On uniform convergence of trigonometric series, Mat. Zametki 81 (2) (2007) 304-310, translation in Math. Notes 81 (2) (2007), 268-274. doi: doi:10.1134/S0001434607010294
- [11] S. Tikhonov, Best approximation and moduli of smoothness: Computation and equivalence theorems, J. Approx. Theory 153 (2008), 19-39. doi: 10.1016/j.jat.2007.05.006 Zbl1215.42002
- [12] A. Zygmund, Trigonometric Series (Cambridge, 2002.e, 2002).

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