Introduction to Pseudo-differential Calculus

Dates: 23/03/2015 - 27/03/2015 (5 sessions)
Time: 9:30 - 11:30 (a total of 10 hours)

This course is mainly oriented toward master students. It provides an introduction to pseudo-differential calculus and semiclassical analysis.

Pseudo-differential calculus is an important tools both in partial differential equations and in quantum mechanics. The main idea is that a very large class of operators on L^2(R^d) can be represented using only functions on R^{2d} called symbols. Many operations can then be done on the level of symbols instead of doing them on operators. An example is the computation of the inverse, which is much simpler for a function than for an operator.

We will introduce pseudo-differential calculus on a simple class of symbols, how to compute with them and give some applications.

PROGRAMME
1. Motivation
2. Basic Notions of Distribution Theory
3. Spaces of Symbols
4. Semiclassical Expansions of Symbols
5. Oscillatory Integrals
6. Pseudodifferential Operators
7. Composition of Pseudodifferential Operators
8. Change of Quantization - Symbolic Calculus
9. Applications

BIBLIOGRAPHY
� Martinez, An Introduction to Semiclassical and Microlocal Analysis.

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