Moderne Analyse - Distributioner og Operatorer

This page gives access to a revised version of the notes used in the courses ModAn in Block 3 and ModAn2 in Block 4, Spring 2007.  They have also been used in earlier courses on Distribution Theory, and they are presently being turned into a book, to appear in the Springer Verlag Graduate Texts in Mathematics series.

 

Lecture Notes:

 (By Gerd Grubb, illustrations made by Mads Haar.)  Latest versions are from December 2007 and Spring 2008.

Contents   (not yet revised) distcon.pdf  distcona.pdf

1. Distribution Spaces   dist1.pdf 

2. Function spaces and approximation    dist2.pdf  

3. Distributions. Examples and rules of calculus    dist3.pdf

4. Realizations and Sobolev spaces   dist4.pdf

5. Fourier transformation of distributions   dist5.pdf

6. Applications to differential operators. The Sobolev Theorem   dist6.pdf

7.  Pseudodifferential operators on open sets    dist7.pdf   dist7n.pdf

8.  Pseudodifferential operators on manifolds, index of elliptic operators dist8.pdf   dist8n.pdf

9.  Boundary value problems in a constant-coefficient case dist9.pdf   dist9n.pdf

10.  Pseudodifferential boundary operators   dist10.pdf dist10n.pdf

11. Pseudodifferential methods for boundary value problems dist11.pdf dist11n.pdf

12. Unbounded linear operators   dist12.pdf

13. (former 12) Families of extensions      dist13b.pdf  dist13n.pdf

14. (former 13)  Semigroups of operators   dist14.pdf

Appendices:

A. Some notation and prerequisites  dista.pdf

B. Topological vector spaces  distb.pdf  

C. Function spaces distc.pdf

References   distrefb.pdf  distrefn.pdf