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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 ...
Greedy approximation for biorthogonal systems in quasi-Banach spaces
(Instytut Matematyczny, 2021)
info:eu-repo/semantics/article,
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems in quasi-Banach spaces from a functional-analytic point of view. If ...
Democracy of quasi-greedy bases in p-Banach spaces with applications to the efficiency of the thresholding greedy algorithm in the hardy spaces Hp(Dd)
(Cambridge University Press, 2023)
Artículo / Artikulua,
We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a -Banach space for 0 < p < p are democratic. The novel techniques we obtain permit to show in particular ...
Quasi-greedy bases in ℓp (0 < p < 1) are democratic
(Elsevier, 2020)
info:eu-repo/semantics/article,
The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to c0, ℓ2, and all separable L1-spaces. ...
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 ...
Building highly conditional almost greedy and quasi-greedy bases in Banach spaces
(Elsevier, 2019)
info:eu-repo/semantics/article,
It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence (k(m)[B](m=1)(infinity) of its conditionality constants verifies the estimate k(m)[B] = O(log m) and that if the reverse ...