The strong \(L^{1}\)- greedy property of the Walsh system

DOI10.3103/S1066369X08050034zbMath1160.42313OpenAlexW2083816556MaRDI QIDQ1006965

Martin G. Grigoryan

Publication date: 26 March 2009

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x08050034

zbMATH Keywords

Walsh systemgreedy algorithmFourier seriesconvergence in the \(L^{1}(0, 1)\)

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Cites Work

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• Quasi-greedy system property of Faber-Schauder subsystems in \(C(0,1)\)
• On nonlinear approximation with respect to the Haar system and modifications of functions
• Dependence of convergence of orthogonal series on changes of values of the function expanded
• On the convergence of Fourier series in the metric of \(L^ 1\)
• Nonlinear methods of approximation
• Some remarks on greedy algorithms
• Divergence of decreasing rearranged Fourier series
• Walsh series and adjustment of functions on small sets
• Greedy approximation with respect to certain subsystems of the Walsh orthonormal system
• On the representation of functions by orthogonal series in weighted $L^p$ spaces
• Mean convergence of orthogonal Fourier series of modified functions
• On the $ L^p_\mu$-strong property of orthonormal systems
• Greedy algorithm for general biorthogonal systems

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