Publication:
The WCGA in Lp(logL)a spaces

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Date
2025
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Authors
Gustavo Garrigós
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Publisher
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Matemáticas
DOI
https://doi.org/10.1007/s00365-023-09664-y
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info:eu-repo/semantics/article
Description
Abstract
We present new results concerning Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm (WCGA) in uniformly smooth Banach spaces X. First, we generalize a result of Temlyakov to cover situations in which the modulus of smoothness and the so called A3 parameter are not necessarily power functions. Secondly, we apply this new theorem to the Zygmund spaces Lp(log L)a , with 1<p<infty and a real, and show that, when the Haar system is used, then optimal recovery of N-sparse signals occurs for a suitable number Phi(N) of iterations, which is sharp when p\leq 2. Finally, an expression for Phi(N) in the case of the trigonometric system is also given.
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Non-linear approximation, greedy algorithm, uniformly smooth Banach space, Orlicz space, Haar system, trigonometric system
Citation
Constr Approx 61, 115–147 (2025).
URI
http://hdl.handle.net/10201/193210
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