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Sparse approximation using new greedy-like bases in superreflexive spaces
(Instytut Matematyczny, 2023)
Artículo / Artikulua,
This paper is devoted to theoretical aspects of optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of non-linear m-term approximation ...
Bidemocratic bases and their connections with other greedy-type bases
(Springer, 2023)
Artículo / Artikulua,
In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this article we shift the viewpoint and study them ...
Weak forms of unconditionality of bases in greedy approximation
(Instytut Matematyczny, 2022)
Artículo / Artikulua,
We study a new class of bases, weaker than quasi-greedy bases, which retain their unconditionality properties and can provide the same optimality for the thresholding greedy algorithm. We measure how far these bases are ...
Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including besov spaces
(Springer, 2023)
Artículo / Artikulua,
We prove that the sequence spaces lp ⊕ lq and the spaces of infinite matrices lp(lq ), lq l(p) and ( ∞ n=1 n lp)lq , which are isomorphic to certain Besov spaces, have an almost greedy basis whenever 0 < p < 1 < q < ∞. ...
Conditional quasi-greedy bases in non-superreflexive Banach spaces
(Springer, 2019)
info:eu-repo/semantics/article,
For a conditional quasi-greedy basis B in a Banach space, the associated conditionality constants km[B] verify the estimate km[B]=O(logm). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied ...
Elton's near unconditionality of bases as a threshold-free form of greediness
(Elsevier, 2023)
Artículo / Artikulua,
Elton's near unconditionality and quasi-greediness for largest coefficients are two properties of bases that made their appearance in functional analysis from very different areas of research. One of our aims in this note ...
Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
(European Mathematical Society, 2019)
info:eu-repo/semantics/article,
We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we ...