21th Internet seminar "Functional calculus" 2017/18

The 21th Internet Seminar on Evolution Equations is devoted to study the theory and applications of functional calculi of (bounded and unbounded) linear operators on Banach spaces.

Roughly speaking, a functional calculus is a consistent way of defining operators of the form for a given operator   and some class of scalar-valued functions such that relations between the functions translate into according relations of the operators .

The most prominent example of such a calculus is the Borel calculus for a self-adjoint operator on a Hilbert space, but many important functional calculi (which allow to cover operator semigroups, fractional powers like the square root of an operator, the operator logarithm) can be constructed under much weaker assumptions on the operator. These functional calculi are of particular importance for the theory of evolution equations, where quite many problems can be reduced to the question whether an operator of the form is bounded or not. Often, this question reduces to a vector-valued singular integral, and hence results from harmonic analysis enter the scene.

The lectures will be on a beginning graduate level. Familiarity with functional analysis and basic complex analysis is assumed, some knowledge of Fourier analysis is helpful but not strictly necessary..

The concept of the “Internet Seminar” originates in 1998 when Rainer Nagel (Tübingen) organized the first Internet Seminar. Since then, many schools have been organized in the same spirit and the experience of the previous editions has shown that these schools are much more effective than traditional schools where participants have a much more passive role. The course is organised in three phases.

• In Phase 1 (October-February), a weekly lecture will be freely accessible over the internet via the ISEM website. The aim of the lectures is to present the theoretic background which lies behind current ongoing research.
• In Phase 2 (April - June), the participants will form small international groups to work on diverse projects which supplement the theory of Phase 1 and provide some applications of it.
• Finally, Phase 3 (30 June - 6 July 2018) consists in a final workshop in Wuppertal, where the teams will present their projects and additional lectures will be delivered by leading experts.

Lecturer

Markus Haase (Kiel)

Organizers

Balint Farkas (Wuppertal)
Bernhard Haak (Bordeaux)
Caren Grenz (Kiel)
Florian Pannasch (Kiel)
Marco Peruzzetto (Kiel)

Website

http://www.math.uni-kiel.de/isem21/en

e-mail