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Pseudodifferential Operators
Last Updated: 2026-02-05 15:19:32
Abstract
The course serves as an introduction to the theory of pseudodifferential operators. The calculus of pseudodifferential operators is developed rigorously using oscillatory integrals. Further topics will include the index of elliptic operators and the local solvability of linear partial differential equations.
Objective
The goal is to present the basic ideas of the theory of linear partial differential operators, aiming at mathematical rigour rather than generality. A further goal is to set the analytical groundwork of pseudodifferential operators needed for a possible followup course/seminar on the Atiyah-Singer index theory.
Content
Distributions and Fourier transform; Pseudodifferential symbols, oscillatory integrals, calculus of PDOs, pseudodifferential operators on manifolds; Local solvability of linear partial differential equations; Elliptic PDOs, parametrices and analytic index;
Resources
Literature
X. Saint Raymond: Elementary introduction to the theory of pseudodifferential operators G.B. Folland: Introduction to partial differential equations L. Hörmander: Linear partial differential operators S.G.Krantz: Partial differential equations and complex analysis
General Information
- Language
- English
- Levels
- DR , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Pseudodifferential Operators
Tuesdays 13:15-15:00 in ML J 34.1
no lectures on 3.4., 1.5., 22.5., and instead there will be additional lectures on the Mondays 2.4., 30.4., 21.5. 10:15-11:55 in HG G 19.1
|
|
2 h weekly |
Offered In
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D-MATH (Official web site of the Zurich Graduate School in Mathematics:)
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