Analysis Prelim Workshop, Fall 2004

Analysis Prelim Workshop, Sep 20-23, 2004

Lecture/discussion sessions: 10 am-12pm, 693 Kerr Hall
Problem solving sessions: 2-4pm, 693 Kerr Hall

Function spaces
- basic measure theory on the real line
- Banach and Hilbert spaces
- weak and strong topologies
- contraction mapping
- Sobolev spaces
linear operators
- dual and adjoint
- self-adjoint and unitary operators
- compact operators; Hilbert Schmidt operators
- weak convergence
- spectral theory
- Green functions
harmonic analysis
- Fourier series and transform
- Sobolev and Rellich embedding theorems
- distributions
- Green functions
calculus of variations
- differential calculus on Banach spaces
- multiple integrals