Translation invariant linear spaces of polynomials

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Translation-invariant linear operators

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, IR or R + which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous...

Nillsen Difference Spaces and Invariant Linear Forms

Shift-Invariant Spaces and Linear Operator Equations

In this paper we investigate the structure of finitely generated shift-invariant spaces and solvability of linear operator equations. Fourier transforms and semi-convolutions are used to characterize shift-invariant spaces. Criteria are provided for solvability of linear operator equations, including linear partial difference equations and discrete convolution equations. The results are then ap...

Approximation by Trigonometric Polynomials in Weighted Rearrangement Invariant Spaces

We investigate the approximation properties of trigonometric polynomials and prove some direct and inverse theorems for polynomial approximation in weighted rearrangement invariant spaces.