Condensation principles with rates
Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces
We show that in a super-reflexive Banach space, the conditionality constants of a quasi-greedy basis ℬ grow at most like 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 for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with .
Conjuntos estrictamente aproximadamente compactos en un espacio normado.
Constructive function theory and spline systems
Continous Norms on Locally Convex Strict Inductive Limit Spaces.
Continuous Position and Existence Sets.
Convergence of approximation processes on convex cones.
Convergence of greedy approximation II. The trigonometric system
We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in the case of...
Convergence of the dual greedy algorithm in Banach spaces.
Convergence theorems for generalized projections and maximal monotone operators in Banach spaces.
Corrigendum on "Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.
Corrigendum to "The Existence and Unicity of Best Approximations".
Criteria for membership of the Besov spaces BS pq.
Darstellungen von Liegruppen und Approximationsprozesse auf Banachräumen.
De nouveaux espaces de Banach sans la propriété d'approximation
Density in the space of topological measures
Topological measures (formerly "quasi-measures") are set functions that generalize measures and correspond to certain non-linear functionals on the space of continuous functions. The goal of this paper is to consider relationships between various families of topological measures on a given space. In particular, we prove density theorems involving classes of simple, representable, extreme topological measures and measures, hence giving a way of approximating various topological measures by members...
Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space
2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.In this paper we consider an L^2 type space of scalar functions L^2 M, A (R u iR) which can be, in particular, the usual L^2 space of scalar functions on R u iR. We find conditions for density of polynomials in this space using a connection with the L^2 space of square-integrable matrix-valued functions on R with respect to a non-negative Hermitian matrix measure. The completness of L^2 M, A (R u iR ) is also established.
Der beschränkte Fall des gewichteten Approximationsproblems für vektorwertige Funktionen.
Die Metrische Struktur der Sonnen in l...(n).
Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space