Weak Greedy Algorithms and the Equivalence Between Semi-greedy and Almost Greedy Markushevich Bases

We introduce and study the notion of weak semi-greedy systems—which is inspired in the concepts of semi-greedy and branch semi-greedy systems and weak thresholding sets-, and prove that in infinite dimensional Banach spaces, the notions of semi-greedy, branch semi-greedy, weak semi-greedy, and almos...

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Vydáno v:The Journal of fourier analysis and applications Ročník 29; číslo 2
Hlavní autoři: Berasategui, Miguel, Lassalle, Silvia
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2023
Springer
Springer Nature B.V
Témata:
Abstract Harmonic Analysis
Algorithms
Approximations and Expansions
Banach spaces
Equivalence
Fourier Analysis
Greedy algorithms
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
Upper bounds
Semi-greedy
Primary 41A65
Almost greedy
46B20
Markushevich
Secondary 46B15
Bases
ISSN:1069-5869, 1531-5851
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Popis
Shrnutí:We introduce and study the notion of weak semi-greedy systems—which is inspired in the concepts of semi-greedy and branch semi-greedy systems and weak thresholding sets-, and prove that in infinite dimensional Banach spaces, the notions of semi-greedy, branch semi-greedy, weak semi-greedy, and almost greedy Markushevich bases are all equivalent. This completes and extends some results from (Berná in J Math Anal Appl 470:218–225, 2019; Dilworth et al. in Studia Math 159:67–101, 2003; J Funct Anal 263:3900–3921, 2012). We also exhibit an example of a semi-greedy system that is neither almost greedy nor a Markushevich basis, showing that the Markushevich condition cannot be dropped from the equivalence result. In some cases, we obtain improved upper bounds for the corresponding constants of the systems.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-023-09997-z