Real Analysis Exchange

Greedy Approximation in Certain Subsystems of the Schauder System

M. G. Grigoryan, A. A. Sargsyan, and R. E. Zink

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Although the sequence of greedy approximants associated with the Schauder expansion of a function, $f$, continuous on $[0,1]$, may fail to converge, there always will be a continuous function, arbitrarily close to $f$, whose Schauder expansion does have a convergent sequence of greedy approximants. Further examination of this problem shows that the same sort of proposition is valid for a multitude of subsystems of the Schauder system.

Article information

Real Anal. Exchange Volume 34, Number 1 (2008), 227-238.

First available in Project Euclid: 19 May 2009

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Mathematical Reviews number (MathSciNet)

Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

greedy algorithm Schauder expansion


Grigoryan, M. G.; Sargsyan, A. A.; Zink, R. E. Greedy Approximation in Certain Subsystems of the Schauder System. Real Anal. Exchange 34 (2008), no. 1, 227--238.

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