Functional Analysis II
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Start of the lecture: Monday, 16.2.2015
Start of the exercise classes: Monday, 23.2.2015
Extract
Spectral
theory, Harmonic Analysis, Weyl's law for eigenfunctions of the (flat)
Laplacian, Unitary representations, and expander networks.
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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.
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Lecture
Exercise Classes
Begins second semester week.
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Christian Beck
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Monday 9-10
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HG F 26.3
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Jonas Luehrmann
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Monday 9-10
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HG G 26.1
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Manuel Luethi
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Monday 9-10
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HG G 26.3
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Series
Sheets can be dropped off at J68.
Lecture History
Week 1
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Sobolev Embedding of Open Sets
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Week 2
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Elliptic Regularity
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Week 3
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Trace Operators
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Week 4
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Weyl's Law / Amenable Groups
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Week 5
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Banach-Tarski / Riesz Representation
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Week 6
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Dirichlet Boundary Problem
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Week 7
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Bochner's Theorem and Spectral Theory of Unitary Operators
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Week 8
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Osterferien
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Week 9
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Spectral Theory of Self-adjoint Operators
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Week 10
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Fourier Transform
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Week 11
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Schwartz Space, Spectral Theory for Unitary 1-Parameter Group, Stone's Theorem
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Week 12
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Expanders and Property (T)
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Week 13
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Banach Algebras
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Script
The lecture will be accompanied by the Lecture Notes on Functional Analysis by M. Einsiedler and T. Ward.
Exam
Information to the exam.