Discrete Translates 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...

APPROXIMATION IN Lp(Rd) FROM SPACES SPANNED BY THE PERTURBED INTEGER TRANSLATES OF A RADIAL FUNCTION

The problem of approximating smooth L p-functions from spaces spanned by the integer translates of a radially symmetric function is very well understood. In case the points of translation, , are scattered throughout R d , the approximation problem is only well understood in the \stationary" setting. In this work, we provide lower bounds on the obtainable approximation orders in the \non-station...

Spaces of Distributions and Interpolation by Translates of a Basis Function

Interpolation with translates of a basis function is a common process in approximation theory. One starts with a single function (the basis function) and a set of interpolation points. The most elementary form of the interpolant then consists of a linear combination of all translates by interpolation points of the basis function. Frequently , low degree polynomials are added to the interpolant....

Approximation by Translates of a Radial Function

Admissible and Singular Translates of Measures on Vector Spaces

We provide a general setting for studying admissible and singular translates of measures on linear spaces. We apply our results to measures on D[0, 1]. Further, we show that in many cases convex, balanced, bounded, and complete subsets of the admissible translates are compact. In addition, we generalize Sudakov's theorem on the characterization of certain quasi-invariant sets to separable refle...