The Weak Chebyshev X-Greedy Algorithm in the unweighted Bergman space

We study a greedy algorithm called the Weak Chebyshev X-Greedy Algorithm (WCXGA) and investigate its application to unweighted Bergman spaces. We first show that the WCXGA converges for a wide class of real and complex Banach spaces and dictionaries. We then prove that certain Bergman spaces and the...

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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 318; H. 2; S. 692 - 706
Hauptverfasser: Dilworth, S.J., Kutzarova, Denka, Shuman, Karen L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: San Diego, CA Elsevier Inc 15.06.2006
Elsevier
Schlagworte:
Bergman space
Exact sciences and technology
Functional analysis
Greedy algorithm
Mathematical analysis
Mathematics
Sciences and techniques of general use
Several complex variables and analytic spaces
Bergman space
Greedy algorithm
Banach space
Mathematical analysis
ISSN:0022-247X, 1096-0813
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Zusammenfassung:We study a greedy algorithm called the Weak Chebyshev X-Greedy Algorithm (WCXGA) and investigate its application to unweighted Bergman spaces. We first show that the WCXGA converges for a wide class of real and complex Banach spaces and dictionaries. We then prove that certain Bergman spaces and their holomorphic monomial dictionaries belong to the class of Banach spaces for which the WCXGA converges.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2005.05.079