Lebesgue-Type Inequalities for Quasi-greedy Bases
Entity
UAM. Departamento de MatemáticasPublisher
Springer New York LLCDate
2013-12-01Citation
10.1007/s00365-013-9209-z
Constructive Approximation 38.3 (2013): 447-470
ISSN
0176-4276 (print); 1432-0940 (online)DOI
10.1007/s00365-013-9209-zFunded by
First and second authors supported by Grant MTM2010-16518 (Spain). Third author supported by a travel grant from Simons Foundation, and by a COR grant from University of California SystemProject
Gobierno de España. MTM2010-16518Editor's Version
http://dx.doi.org/10.1007/s00365-013-9209-zSubjects
Bounded variation; Democracy functions; Lebesgue-type inequalities; Non-linear approximation; Quasi-greedy bases; Thresholding greedy algorithm; MatemáticasNote
The final publication is available at Springer via http://dx.doi.org/10.1007/s00365-013-9209-zRights
© Springer Science+Business Media New York 2013Abstract
We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N-term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C log N. We show with two examples that this bound is attained for quasi-greedy democratic bases
Files in this item
Google Scholar:Garrigós, Gustavo
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Hernández Rodríguez, Eugenio
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Oikhberg, Timur
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