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

Abstract

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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.

How to cite

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Radosława 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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  2. [2] A.D. Bailey, Almost Everywhere Convergence of Dyadic Partial Sums of Fourier Series for Almost Periodic Functions, Master of Philosophy, A thesis submitted to School of Mathematics of The University of Birmingham for the degree of Master of Philosophy, September, 2008. 
  3. [3] A.S. Besicovitch, Almost Periodic Functions (Cambridge, 1932). 
  4. [4] L. Leindler, On the uniform convergence and boundedness of a certain class of sine series, Analysis Math. 27 (2001), 279-285. doi: 10.1023/A:1014320328217 Zbl1002.42002
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  7. [7] B.L. Levitan, Almost periodic functions, Gos. Izdat. Tekh-Teoret. Liter. (Moscov, 1953) in Russian. 
  8. [8] P. Pych-Taberska, Approximation properties of the partial sums of Fourier series of almost periodic functions, Studia Math. XCVI (1990), 91-103. 
  9. [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. [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. [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. [12] A. Zygmund, Trigonometric Series (Cambridge, 2002.e, 2002). 

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