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401-4472-00L 5 Credits DR , MSC D-USYS , D-MAVT , D-MTEC , D-MATH , D-BIOL , D-CHAB

Pseudodifferential Operators

Lecturers & Examiners: Dr. László Székelyhidi
VVZ CR n/a

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
  • Tue 13:15-15:00 (ML J 34.1)
  • Tue 14:15-15:00 (HG E 33.3)
  • 02.04 Date 10:15-12:00 (HG G 19.1)
  • 30.04 Date 10:15-12:00 (HG G 19.1)
  • 21.05 Date 10:15-12:00 (HG G 19.1)
2 h weekly

Offered In