Authors:
G. Dzyubenko International Mathematical Center of NAS of Ukraine 01601 Tereschenkivs’ka str., 3 Kyiv Ukraine

Search for other papers by G. Dzyubenko in
Current site
Google Scholar
PubMed
Close
and
J. Gilewicz Toulon University and Centre de Physique Théorique, CNRS — Luminy, Case 907 13288 Marseille Cedex 09 France

Search for other papers by J. Gilewicz in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract  

Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points yiY:= {yi}i∈ℤ such that for x ∈ [yi, yi−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each nN(Y) we construct a trigonometric polynomial Pn of order ≦ n, changing its sign at the same points yiY as f, and

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\| {f - P_n } \right\| \leqq c(s)\omega _3 \left( {f,\frac{\pi } {n}} \right),$$ \end{document}
where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s, ω3(f, t) is the third modulus of smoothness of f and ∥ · ∥ is the max-norm.

  • Collapse
  • Expand

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Dec 2023 8 0 2
Jan 2024 6 0 2
Feb 2024 0 0 0
Mar 2024 5 0 0
Apr 2024 14 0 0
May 2024 12 0 0
Jun 2024 0 0 0