Harmonic Analysis

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

This course will introduce the basics of harmonic analysis on Euclidean spaces. Topics covered include the maximal operator, basic interpolation theorems, Hilbert transform, weighted inequalities, H1 and BMO spaces, singular integral operators, and Littlewood-Paley theory. In addition, emphasis will be placed on connections to complex analysis and analysis of partial differential equations.

Requirements:

Syllabus of lectures:

Outline:

1. Maximal operator.

2. Basic interpolation theorems.

3. Hilbert transform.

4. Weighted inequalities.

5. H1 and BMO spaces.

6. Singular integral operators.

7. Littlewood-Paley theory.

Syllabus of tutorials:

Study Objective:

The student will become familiar with the classical parts of harmonic analysis, the most commonly used operators and function spaces. Emphasis will also be placed on the use of harmonic analysis in Fourier analysis, theory of partial differential equation, and complex analysis.

Study materials:

1.E. M. Stein: Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N. J., 1970.

2.E. M. Stein and G.Weiss: Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N. J., 1971.

3.J. Duoandikoetxea: Fourier Analysis, Crm Proceedings & Lecture Notes, American Mathematical Society, 2001.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: