Lebesgue-Type Inequalities for Quasi-greedy Bases

By Gustavo Garrigós, Eugenio Hernández, Timur Oikhberg. 2011

54 citations recorded by the source corpus.

We show that, for quasi-greedy bases in real or complex Banach spaces, an optimal bound for the ratio between greedy N-term approximation ∥x−GNx∥ and the best N-term approximation σN(x) is controlled by max{μ(N),kN}, where μ(N) and kN are well-known constants that quantify the democracy and conditionality of the basis. In particular, for democratic bases this bound is O(logN). We show with various examples that these bounds are actually attained.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9ff91f7c6b682fbde400d7b08df949124c59115a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Pablo M. Berná
2. Gustavo Garrigós
3. Fernando Albiac
4. José L. Ansorena
5. Ó. Blasco
6. Przemyslaw Wojtaszczyk
7. Vladimir N. Temlyakov
8. Morten Nielsen

In Mathematical Physics

1. Pablo M. Berná
2. José L. Ansorena
3. Gustavo Garrigós
4. Fernando Albiac
5. Ó. Blasco
6. Przemyslaw Wojtaszczyk
7. Vladimir N. Temlyakov
8. Rémi Gribonval

In Numerical Analysis

1. Pablo M. Berná
2. Przemyslaw Wojtaszczyk
3. José L. Ansorena
4. Ó. Blasco
5. Fernando Albiac
6. Gustavo Garrigós

Citations in the corpus

• Lebesgue inequalities for the greedy algorithm in general bases (2016, methodology): “Our contribution here is an improvement of the implicit constants in the second summand, compared to O(q(4)) in [9], and 8q(3) in [6].”
• Greedy approximation for biorthogonal systems in quasi-Banach spaces (2019, background): “3] is the case KT[l2], while KT[lp], 1 < p < ∞, was later considered in [44].”