Banach Journal of Mathematical Analysis

On convergence of greedy approximations for the trigonometric system

Sergei V. Konyagin

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Abstract

In this note we discuss the convergence of greedy approximants for trigonometric Fourier expansion in $L_p(\mathbb{T})$, $1\leq p \leq2, p \neq 2$.

Article information

Source
Banach J. Math. Anal., Volume 1, Number 2 (2007), 208-211.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336217

Digital Object Identifier
doi:10.15352/bjma/1240336217

Mathematical Reviews number (MathSciNet)
MR2366102

Zentralblatt MATH identifier
1134.42300

Subjects
Primary: 42A10: Trigonometric approximation
Secondary: 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Keywords
trigonometric Fourier series greedy approximation

Citation

Konyagin, Sergei V. On convergence of greedy approximations for the trigonometric system. Banach J. Math. Anal. 1 (2007), no. 2, 208--211. doi:10.15352/bjma/1240336217. https://projecteuclid.org/euclid.bjma/1240336217


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References

  • A. Cordoba and P. Fernandez, Convergence and divergence of decreasing rearranged Fourier series, SIAM, I. Math. Anal. 29 (1998), 1129–1139.
  • S.V. Konyagin and V.N. Temlyakov, Convergence of greedy approximation II. The trigonometric system, Studia Math. 159 (2003), 161–184.
  • S.V. Konyagin and V.N. Temlyakov, Convergence of greedy approximation for the trigonometric system, Analys. Math. 31 (2005), 85–115.
  • J.F. Méla, Mesures $\varepsilon$-idempotentes de norme born'ee\j, Studia Math. 72 (1982), 131–149.
  • V.N. Temlyakov, Greedy algorithm and $m$-term trigonometric approximation, Constr. Approx. 107 (1998), 569–587.
  • V.N. Temlyakov, Nonlinear methods of approximation, IMI Preprint series 9 (2001), 1–57.