Interpolation Theory

Lecture

The lecture will be held by Dr. Markus Hansen. It takes place every Tuesday on 1pm - 3pm and on Friday 3pm - 4pm at HG E33.5.

Literature

The three main references for Interpolation theory are:

1) C. Bennett and R. Sharpley: Interpolation of operators. Academic Press, 1988.

2) J. Bergh and J. Löfström: Interpolation spaces. An Introduction. Springer, 1976.

3) H. Triebel: Interpolation Theory, Function Spaces, Differential Operators. North-Holland, 1978.

The most important research articles for this topic are:

1) J.L. Lions and J. Peetre: Sur une classe d'espaces d'interpolation.
Inst. Hautes Etudes Sci. Publ. Math. 19 (1964), 5–68.

2) A. Calderon: Intermediate Spaces and Interpolation, complex method.
Studia Math. 24 (1964), 113-190.

3) J. Peetre and G. Sparr: Interpolation of normed abelian groups.
Ann. Mat. Pura Appl. 92 (1972), 217–262.

Exercises

There will be no exercises. Though sometimes parts of proofs will be left open as exercises, no written solution is required, and those arguments will be provided in the script.

If necessary (in particular for Master students) there will be oral exams, with dates per agreement.

Script

The script will be provided chapterwise shortly after completing the respective sections in the lecture.

Chapter 1
(The interpolation theorems of Riesz-Thorin and Marcinkiewicz and some applications.)

Chapters 1 and 2 (v2 04.11.)
(Basics on quasi-Banach spaces and abstract interpolation theory.)

Chapters 1 - 3.2 (14.11.)
(The K-method and interpolation of sequence spaces)

Chapters 1 - 4.2 (24.01.)
(The J-method and reiteration theorem)