Six Lectures on translation-invariant operators and subspace

Abstract

This paper represents the text of a minicourse delivered by the author for participants of the \textquotedbl{}Workshop on Measure Theory and Real Analysis\textquotedbl{}, Grado, September-97. We consider topics on multiplier theory and translation-invariant subspaces in function spaces on groups $\mathbb{T}$ and $\mathbb{Z}$. Our goal is to give an introduction to the subject from the very beginning up to some recent results. The presentation is aimed at graduate students; no preliminaries in Fourier Analysis are supposed.