In this paper we study the behavior of best Lp-approximations by rational functions to an analytic function on union of disks, when the measure of them tends to zero.

Let D be the unit disk. We show that for some relatively closed set F ⊂ D there is a function f that can be uniformly approximated on F by functions of H∞, but such that f cannot be written as f = h + g, with h ∈ H∞ and g ...

We introduce a concept of best local approximation using abstract norms and non-homogeneous dilations. The asymptotic behavior of the normalized error function as well as the limit of some net of best approximation polynomials ...

In this paper, we extend results given by Z´o and Cuenya in 2007 about a general approach to problems of best vector-valued approximation on small regions from a finite dimensional subspace of polynomials of some degree. ...

The notion of p-compact sets arises naturally from Grothendieck´s characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the ...

In this paper we study a maximal operator Mf related with the best ϕ approximation by constants for a function f ∈ L ϕ 0 loc(ℝn), where we denote by ϕ 0 for the derivative function of the C1 convex function ϕ. We get a ...

This paper is dealing with the problem of finding the best multipoint Padé approximant of an analytic function when data in some neighborhoods of sampling points are more important than others. More exactly, we obtain a ...

Given an Ap-Muckenhoupt weight on a fractal obtained as the attractor of an iterated function system, we construct a sequence of approximating weights, which are simple functions belonging uniformly to the Ap class on the ...

We consider perturbation of frames and frame sequences in a Hilbert space. It is known that small perturbations of a frame give rise to another frame. We show that the canonical dual of the perturbed sequence is a perturbation ...

Let Γ be a crystal group in Rd. A function φ:Rd⟶C is said to be crystal-refinable (or Γ-refinable) if it is a linear combination of finitely many of the rescaled and translated functions φ(γ−1(ax)), where the translationsγ ...