Pointwise strong approximation of almost periodic functions
Radosława Kranz ; Włodzimierz Łenski ; Bogdan Szal
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 36 (2016), p. 45-63 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:286887
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     title = {Pointwise strong approximation of almost periodic functions},
     journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
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     year = {2016},
     pages = {45-63},
     zbl = {1261.42003},
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Radosława Kranz; Włodzimierz Łenski; Bogdan Szal. Pointwise strong approximation of almost periodic functions. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 36 (2016) pp. 45-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1178/

[000] [1] A. Avantaggiati, G. Bruno and B. Iannacci, The Hausdorff-Young theorem for almost periodic functions and some applications, Nonlinear Analysis, Theory, Methods and Applications 25 (1) (1995), 61-87. | Zbl 0844.42006

[001] [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.

[002] [3] A.S. Besicovitch, Almost Periodic Functions (Cambridge, 1932).

[003] [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 | Zbl 1002.42002

[004] [5] L. Leindler, A new extension of monotone sequence and its application, J. Inequal. Pure and Appl. Math. 7 (1) (2006) Art. 39, pp. 7. | Zbl 1132.26304

[005] [6] W. Łenski, Pointwise strong and very strong approximation of Fourier series, Acta Math. Hung. 115 (3), 207, 215-233. | Zbl 1136.41004

[006] [7] B.L. Levitan, Almost periodic functions, Gos. Izdat. Tekh-Teoret. Liter. (Moscov, 1953) in Russian.

[007] [8] P. Pych-Taberska, Approximation properties of the partial sums of Fourier series of almost periodic functions, Studia Math. XCVI (1990), 91-103.

[008] [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 | Zbl 1106.42003

[009] [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

[010] [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 | Zbl 1215.42002

[011] [12] A. Zygmund, Trigonometric Series (Cambridge, 2002.e, 2002).