Harmonic Analysis on Commutative Spaces

What it is about

You will learn the fundamentals of harmonic analysis on topological groups and on their coset spaces. You will practice integration and convolution on groups, fundamentals of representation theory and specific techniques for Abelian, compact as well as homogeneous spaces and double coset spaces. In the end you will be able to analyze functions on these spaces and understand the connections to geometric analysis.

What you will be able to do

• Understanding topological groups
• Applying integration on topological groups and convolution
• Foundations of representation theory and related group algebras
• Harmonic analysis on Abelian and compact groups
• Harmonic analysis on homogeneous spaces and double coset spaces
• Treatment and understanding of spherical functions
• Relating to noncommutative analysis and geometric analysis

What the module consists of

• VorlesungTransmission of content through lecture, examples and discussion
• Übung/Practice sessionsDeepening through problem sheets, solutions and supervised or increasingly independent work in small groups

Teaching method

• VorlesungPresentation of content, motivation and discussion with students
• Übungen mit Aufgaben und LösungenDeepening of understanding and independent verification of learning progress; initially supervised, then increasingly independent work