Interpolation problems in function spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On some interpolation problems in polynomial spaces with generalized degree

The aim of this paper is to study many interpolation problems in the space of polynomials of w-degree n. In order to do this, some new results concerning the polynomial spaces of w-degree are given. In this article, we consider only the case of functions in two variables. More details are obtained for the weight w = (1, w2). We found a set of conditions for which, Πn,w, the space of polynomials...

Radial Basis Function Interpolation in Sobolev Spaces and Its Applications

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H(Ω) (k ≥ 1). With a special kind of radial basis function, we construct a basis in H(Ω) and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density. Mathematics subject classification: 41...

Short Lecture Notes: Interpolation Theory and Function Spaces

Differentials of Complex Interpolation Processes for Kothe Function Spaces

We continue the study of centralizers on Kothe function spaces and the commutator estimates they generate (see [29]). Our main result is that if X is a super-reflexive Kothe function space then for every real centralizer Q on X there is a complex interpolation scale of Kothe function spaces through X inducing Q as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, al...