The degree of approximation by Hausdorff means of a conjugate Fourier series
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2.

Voir la notice de l'article provenant de la source Library of Science

The purpose of this paper is to analyze the degree of approximation of a function f that is a conjugate of a function f belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.
Keywords: Hausdorff matrix, conjugate series of the Fourier series, degree of approximation
@article{AUM_2016_70_2_a6,
     author = {K\k{e}ska, Sergiusz},
     title = {The degree of approximation by {Hausdorff} means of a conjugate {Fourier} series},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a6/}
}
TY  - JOUR
AU  - Kęska, Sergiusz
TI  - The degree of approximation by Hausdorff means of a conjugate Fourier series
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2016
VL  - 70
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a6/
LA  - en
ID  - AUM_2016_70_2_a6
ER  - 
%0 Journal Article
%A Kęska, Sergiusz
%T The degree of approximation by Hausdorff means of a conjugate Fourier series
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2016
%V 70
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a6/
%G en
%F AUM_2016_70_2_a6
Kęska, Sergiusz. The degree of approximation by Hausdorff means of a conjugate Fourier series. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 70 (2016) no. 2. http://geodesic.mathdoc.fr/item/AUM_2016_70_2_a6/

[1] Hardy, G. H., Divergent Series, Clarendon Press, Oxford, 1949.

[2] Hausdorff, F., Summationsmethoden und Momentfolgen, Math. Z. 9 (1921), I: 74-109, II: 280–289.

[3] Hildebrandt, T. H., Schoenberg, I. J., On linear functional operations and the moment problem for a finite interval in one or several dimensions, Ann. of Math. 34 (1933), 317-328.

[4] Jakimovski, A., The sequence-to-function analogues to Hausdorff transformations, Bulletin of the Research Council of Israel vol. 8, 1959 (1960).

[5] Kęska, S., A variant of the Hausdorff theorem for multi-index matrices II, Linear Algebra Appl. 327 (2001), 17-26.

[6] Lal, S., Approximation of conjugates of almost Lipschitz functions by matrix Cesaro summability method, Arab. J. Math. Sci. 10 (2) (2004), 54.

[7] Lal, S., Mishra, A., Euler-Hausdorff matrix summability operator and trigonometric approximation of the conjugate of a function belonging to the generalized Lipschitz class, J. Inequal. Appl. (2013), 2013:59.

[8] Privalov, I. I., Sur les fonctions conjuguees, Bull. Soc. Math. France 44 (1916), 100-103.

[9] Qureshi, K., On the degree of approximation of function belonging to the Lipschitz class by means of a conjugate series, Indian J. Pure Appl. Math. 12 (9) (1981), 1120-1123.

[10] Rhoades, B. E., Ozkoklu, Kevser, Albayrak, Inci, On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series, Appl. Math. Comput. 217 (2011), 6868-6871.

[11] Toeplitz, O., Uber allgemeine lineare Mittelbildungen, Prace Matematyczno-Fizyczne 22 (1911), 111-119.