Microlocal and Semiclassical Analysis

• 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

Date and time info
Tuesday 17:15 - 18:45, Wednesday 11:15 - 12:45

Prerequisites
Analysis I-II, Linear Algebra I-II, Measure and Integration Theory. Ideally: Functional Analysis, Differential Geometry