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Functional Analysis II

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Start of the lecture: Monday, 16.2.2015
Start of the exercise classes: Monday, 23.2.2015

Lecturer
Prof. Manfred Einsiedler
Coordinator Rene Rühr

Extract

Spectral theory, Harmonic Analysis, Weyl's law for eigenfunctions of the (flat) Laplacian, Unitary representations, and expander networks. The student will learn the spectral theory of operators on Hilbert spaces, Fourier analysis from a more general view point, and other more sophisticated tools of functional analysis, e.g. Choquet's theorem, amenable groups, and groups with property (T). Another goal is to see the importance of functional analysis in many other mathematical areas like partial differential equations, theory of expanders, and number theory.

Lecture

Monday 10 - 12 HG G 5
Thursday 1 - 3
HG G 5

Exercise Classes

Begins second semester week.

  Christian Beck
Monday 9-10 HG F 26.3
  Jonas Luehrmann
Monday 9-10
HG G 26.1
  Manuel Luethi
Monday 9-10 HG G 26.3

Series

Sheets can be dropped off at J68.

Lecture History

Week 1
Sobolev Embedding of Open Sets
Week 2
Elliptic Regularity
Week 3
Trace Operators
Week 4
Weyl's Law / Amenable Groups
Week 5 Banach-Tarski / Riesz Representation
Week 6
Dirichlet Boundary Problem
Week 7
Bochner's Theorem and Spectral Theory of Unitary Operators
Week 8
Osterferien
Week 9
Spectral Theory of Self-adjoint Operators
Week 10
Fourier Transform
Week 11
Schwartz Space, Spectral Theory for Unitary 1-Parameter Group, Stone's Theorem
Week 12
Expanders and Property (T)
Week 13
Banach Algebras

Script

The lecture will be accompanied by the Lecture Notes on Functional Analysis by M. Einsiedler and T. Ward.

Exam

Information to the exam.

 

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