Entropy function spaces and interpolation

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...

Entropy and Multivariable Interpolation

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

Short Lecture Notes: Interpolation Theory and Function Spaces

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...

Entropy Numbers in Weighted Function Spaces and Applications

We intend to give a rather brief summary of recent investigations concerning entropy numbers in weighted function spaces. For the sake of brevity we will restrict ourselves to some special \model" cases. We will thus always refer to the original papers 3], 4] and 5] for details and generalizations. Most of the presented results have been obtained in a joint work with Prof. H. Triebel.