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Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

F. Albiac, J. L. Ansorena, G. Garrigós, E. Hernández, M. Raja (2015)

Studia Mathematica

We show that in a super-reflexive Banach space, the conditionality constants k N ( ) of a quasi-greedy basis ℬ grow at most like O ( ( l o g N ) 1 - ε ) for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in L p for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with k N ( ) l o g N .

Constants of strong uniqueness of minimal norm-one projections

A. Micek (2011)

Banach Center Publications

In this paper we calculate the constants of strong uniqueness of minimal norm-one projections on subspaces of codimension k in the space l ( n ) . This generalizes a main result of W. Odyniec and M. P. Prophet [J. Approx. Theory 145 (2007), 111-121]. We applied in our proof Kolmogorov’s type theorem (see A. Wójcik [Approximation and Function Spaces (Gdańsk, 1979), PWN, Warszawa / North-Holland, Amsterdam, 1981, 854-866]) for strongly unique best approximation.

Construction de bases d'ondelettes α-höldériennes.

Albert Cohen (1990)

Revista Matemática Iberoamericana

Dans cet article, nous reprenons une méthode due à Ingrid Daubechies pour générer des bases orthonormales de fonctions dans L2(R) de la forme {2j/2 ψ (2jx - k)}j,k ∈ Z à partir de filtres miroir en quadrature (QMF) tels que l'ondelette ψ ait de bonnes propriétés de régularité. Une estimation de l'exposant de Hölder global optimal est obtenue en caractérisant précisément la decroissance de la fonction ψ'. Nous précisons finalement les liens exacts entre la régularité de l'ondelette et son ordre de...

Constructions of interpolation curves from given supporting elements. I

Josef Matušů, Josef Novák (1985)

Aplikace matematiky

This paper deals with the constructions of interpolation curves which pass through given supporting points (nodes) and touch supporting tangent vectors given at only some fo these points or, as the case may be, at all these points. The mathematical kernel of these constructions is based on Lienhard's interpolation method.

Constructions of interpolation curves from given supporting elements. II

Josef Matušů, Josef Novák (1986)

Aplikace matematiky

This paper deals with the constructions of interpolation curves which pass through given supporting points (nodes) and touch supporting tangent vectors given at only some of these points or, as the case may be, at all these points. The mathematical kernel of these constructions is based on the Lienhard's interpolation method. Formulae for the curvature of plane and space interpolation curves are derived.

Containing l1 or c0 and best approximation.

Juan Carlos Cabello Piñar (1990)

Collectanea Mathematica

The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.

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