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

S. J. Dilworth; Denka Kutzarova; Karen L. Shuman

doi:10.1016/j.jmaa.2005.05.079

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

S. J. Dilworth, Denka Kutzarova, Karen L. Shuman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	692-706
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	318
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2005.05.079
State	Published - Jun 15 2006

Keywords

Bergman space
Greedy algorithm

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jmaa.2005.05.079

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title = "The Weak Chebyshev X-Greedy Algorithm in the unweighted Bergman space",

abstract = "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.",

keywords = "Bergman space, Greedy algorithm",

author = "Dilworth, {S. J.} and Denka Kutzarova and Shuman, {Karen L.}",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (S.J. Dilworth), [email protected] (D. Kutzarova), [email protected] (K.L. Shuman). 1 Current address: Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA. 2 Partially supported by UIUC NSF VIGRE grant DMS-98-83160 during the work on this paper.",

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doi = "10.1016/j.jmaa.2005.05.079",

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T1 - The Weak Chebyshev X-Greedy Algorithm in the unweighted Bergman space

AU - Dilworth, S. J.

AU - Kutzarova, Denka

AU - Shuman, Karen L.

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (S.J. Dilworth), [email protected] (D. Kutzarova), [email protected] (K.L. Shuman). 1 Current address: Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA. 2 Partially supported by UIUC NSF VIGRE grant DMS-98-83160 during the work on this paper.

PY - 2006/6/15

Y1 - 2006/6/15

N2 - 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.

AB - 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.

KW - Bergman space

KW - Greedy algorithm

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

Abstract

Keywords

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