room: A1-33, godz. 10:30–12:00

Jurgen Appell (University of Wurzburg)
Condensing Operators: a Friendly Introduction

Summary. The definition of condensing operators is based on the notion of measures of noncompactness and provides a natural generalization of compact operators. So it is not surprising that various attempts have been made to carry over important features of both compact linear operators (spectral theory, Fredholm theory, etc.) and nonlinear operators (fixed point theory, degree theory, etc.) to this operator class. Although the theory of condensing operators is nowadays quite advanced and well-established, there is still a deplorable lack of applications. The main purpose of the talk will be to discuss, after briefly summarizing the basic theoretical definitions and results, some typical applications arising in various fields of mathematical analysis. Such applications refer to Hilbert transforms, Sturm-Liouville problems, Schrödinger equations, composition operators on Bergman spaces, and others. As the title suggests, the talk will require only a modest background in functional analysis and operator theory, and therefore will be accessible also to PhD students.

Tea and coffee at 10:00.