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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Abstract

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

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

Dates
First available in Project Euclid: 19 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.rae/1242738934

Zentralblatt MATH identifier
05578228

Mathematical Reviews number (MathSciNet)
MR2527136

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

Keywords
greedy algorithm Schauder expansion

Citation

Grigoryan, M. G.; Sargsyan, A. A.; Zink, R. E. Greedy Approximation in Certain Subsystems of the Schauder System. Real Analysis Exchange 34 (2008), no. 1, 227--238. http://projecteuclid.org/euclid.rae/1242738934.


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References

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