Geodesic
Approximation properties of partial Fourier sums in the $p$-variation metric
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 29-35

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we examine the degree of approximation by Fourier partial sums in the $p$-variational norm. We propose two criteria for convergence of these sums with a given rate in terms of growth of the norms of the differentiated Fourier partial sums. Also, we establish the relationship between the approximation of a function and its conjugate function.
Keywords: function of bounded $p$-variation, partial Fourier sums, derivative, conjugate function.
Mots-clés : convergence rate 
@article{INTO_2021_200_a2,
     author = {S. S. Volosivets and A. A. Tyuleneva},
     title = {Approximation properties of partial {Fourier} sums in the $p$-variation metric},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {29--35},
     publisher = {mathdoc},
     volume = {200},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_200_a2/}
}
TY  - JOUR
AU  - S. S. Volosivets
AU  - A. A. Tyuleneva
TI  - Approximation properties of partial Fourier sums in the $p$-variation metric
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 29
EP  - 35
VL  - 200
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_200_a2/
LA  - ru
ID  - INTO_2021_200_a2
ER  - 
%0 Journal Article
%A S. S. Volosivets
%A A. A. Tyuleneva
%T Approximation properties of partial Fourier sums in the $p$-variation metric
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 29-35
%V 200
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_200_a2/
%G ru
%F INTO_2021_200_a2
S. S. Volosivets; A. A. Tyuleneva. Approximation properties of partial Fourier sums in the $p$-variation metric. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 29-35. http://geodesic.mathdoc.fr/item/INTO_2021_200_a2/