Interpolation Theory

In this lecture we present the classical theory of interpolation of Banach spaces. Starting with the theorem of Riesz-Thorin and its immediate application to some famous operators, we concentrate then on the real methods, the so-called $K$- and $J$-methods. As a major application we show the interpolation of Sobolev- and Besov spaces with a short introduction to function spaces. If time allows, we present a further application to quantitative approximation theory in terms of entropy- and approximation numbers. This lecture will be a 2 SWS course held in english and is recommended for PhD students or students of higher semesters with interests in higher analysis.