Class number: 250085
Class type: VO (lecture course)
Semester hours: 3
Time and place: Mon 13:15--14:45 2A310 (UZA 2);
Thu 13:15--14:45 2A310 (UZA 2)
Start: 5.10.2009
News:
2009-10-23: The mastercopy of chapters 0 and 1 is available at my office door.
2009-10-16: There will be no lecture on Thu, Oct. 29.
2009-10-13: The monday lectures will have been shifted by ten minutes and
will now start at 13:05 hence end at 14:35.
General introduction: The theory of pseudodifferential operators
emerged in the mid 1960-ies through the work of Kohn and Nirenberg and
has earlier roots in Fourier analysis and singular integrals. It was
subsequently refined by a number of mathematicians, most notably by Lars Hörmander, and turned into one of the most
esstential tools in PDE. More precisely, it allows a flexible way of
applying Fourier techniques to the study of variable-coefficient operators
and singularities of distributions. By the latter we mean the wave front set, a
refinement of the notion of singular support, in the sense that also the
the "bad frequency directions'' of the distribution are taken into account---the
study of which is called microlocal analysis.
Applications of pseudodifferential operators are multitude. The most
prominent and classical is the propagation of the wave front set for
solutions of partial differential equations. However, over the years,
in particular pseudodifferential calculus has turned into a general method that
has successfully been applied in diverse fields of analysis, recently also
in time frequency analysis.
For a (slightly) more technical introduction and an outline
of the main aims of the course click here.
Contents: At least for the first three quarters of the course we
will rather closely follow the book Elementary Introduction to the Theory
of Pseudodifferential Operators by Xavier Saint Raymond (Studies in
Mathematics, CRC-Press, Boca Raton, 1991). The main chapters will be: