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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

Lecture Note

Interpolation theory and approximation issues in function spaces

Jan Schneider


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.