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Lecture Note
43/2013
Interpolation theory and approximation issues in function spaces
Jan Schneider
Abstract
This one-semester lecture is suitable for graduate students, PhD students and postdocs with background in analysis. It is meant to be a course of two hours per week and aims to present a specific point of view on the terms interpolation and approximation, which are sometimes used with a very different meaning.
In chapter 1 we present the classical real interpolation theory with focus on the so-called $K$- and $J$-methods. Chapter 2 is a very brief excursion to the theory of function spaces, including a short historical survey until the 1970s (Besov spaces). Here we provide the reader with one of the main applications of interpolation theory and the necessary background for chapter 3. This last chapter is dedicated to a very specific aspect of approximation theory in function spaces, related to compactness of operators. Although a self-contained topic, it is also connected to interpolation theory as we will point out.
