Mathematisches Seminar: Pseudodifferential operators
Time: Wednesday 10 – 12 Room: B 252
First meeting: Mon 18/10/10, 14:00 in B 448
(Discussion of topics and assignment of talks)
If you are interested in participating please contact me by email before the first meeting —
talks can be given in English or German!
Synopsis
Pseudodifferential operators are a generalisation of differential operators
which have emerged in the 1960ies and proved useful in
many arenas of modern analysis and mathematical physics. They are particularly important
to the study of elliptic partial differential equations and in the index theory for elliptic operators. Pseudodifferential operators
allow not only to establish new theorems but also to have a fresh look
at old ones and thereby obtain simpler and more transparent formulations of already known
facts.
The goal of the seminar is to provide an introductory overview of this highly developed field without getting involved into too many technicalities.
The seminar also includes an introduction to Fourier transforms and distributions, which are abundant in analysis and its applications.
Audience
3rd year Bachelor students and Master students of Mathematics and Physics, TMP students
Prerequisites
Analysis I – III, basic knowledge of functional analysis
Topics to be discussed
- Fourier transform
- Distributions
- Fractional Sobolev spaces
- Global regularity of elliptic partial differential equations
Literature
- M. M. Wong, An Introduction to pseudo-differential Operators , 2nd ed., World Scientific, Singapore, 1999.
- B. E. Petersen, Introduction to the Fourier transform and pseudo-differential operators, Pitman, Boston, 1983
- X. Saint Raymond, Elementary introduction to the theory of pseudodifferential operators, CRC Press, Boca Raton, 1991
- L. Hörmander, The analysis of linear partial differential operators III, pseudo-differential operators, corr. reprint, Springer, Berlin, 1994.
- M. Shubin, Pseudodifferential operators and spectral theory, 2nd ed., Springer, Berlin, 2001.