Tuesday 17:15 – 18:45, SG 3-10
Wednesday 11:15 – 12:45, Augusteum, A-314
Lecture notes
Will be provided and updated on a weekly basis after the beginning of the course. Our main references will be the first two mentioned in the Literature section below.
Contents
- Test functions, Schwartz functions, distributions: tempered distributions, regular and singular distributions, compactly supported distributions
- Distributional derivatives and further operations with distributions
- Wavefront set and singular support, products of distributions
- Oscillatory integrals, symbol classes, pseudodifferential operators
- (Semiclassical) quantisation and symbol calculus
- Ellipticity, parametrix construction
- Sobolev spaces, Fredholm theory
- Schwartz kernel theorem, operator wavefront set, microlocalisation
Requirements
Analysis I-II, Linear Algebra I-II, Measure and Integration Theory. Ideally: Functional Analysis, Differential Geometry
Literature
Peter Hintz, An Introduction to Microlocal Analysis
Thibault Lefeuvre, Microlocal Analysis in Hyperbolic Dynamics and Geometry
Semyon Dyatlov & Maciej Zworski, Mathematical Theory of Scattering Resonances (Appendices)
Michail A. Shubin, Pseudodifferential Operators and Spectral Theory
Maciej Zworski, Semiclassical Analysis