Introduction to Harmonic Analysis, Spring 2016.

Lecture:

Wednesday, 8:15-10:00 in HG F 26.5

Question times ("Präsenz"):

Monday, 14:00 – 15:00, in HG G 49.1 or by appointment.

Course content:

This is an introductory course on Harmonic Analysis. During the semester, we will study the Fourier transform, Interpolation of operators, Maximal functions, Calderon-Zygmund theory, and Littlewood-Paley theory. This course is primarily given to Bachelor's and Master's students in Mathematics. A prerequisite for the class is a semester of Real Analysis. Prior knowledge of Fourier transform techniques is helpful, but not necessary, as the course is planned to be self-contained.

Lecture Notes:

Lecture Notes 1: The Fourier transform.

Lecture Notes 2: Interpolation theory.

Lecture Notes 3: Maximal functions.

Lecture Notes 4: Singular integral operators.

Bonus Lecture Notes: Littlewood-Paley theory.

References:

There is no required textbook for the course. The following references are useful:

Duoandikoetxea, J. : "Fourier Analysis", AMS Graduate Studies in Mathematics, Vol. 29 (2001).

Grafakos, L. : "Classical and Modern Fourier Analysis", Pearson/Prentice Hall (2004).

Stein, E. M., with the assistance of Murphy, T. S. : "Harmonic Analysis, Real-variable Methods, Orthogonality, and Oscillatory Integrals", Princeton University Press (1993).

Stein, E. M. : "Singular Integral Operators and Differentiability Properties of Functions", Princeton University Press (1986).

Stein, E. M., Weiss, G. : "Fourier Analysis on Euclidean Spaces", Princeton University Press (1971).

Stein, E. M., Shakarchi. R. : "Fourier Analysis: An introduction", Princeton Lectures in Analysis I (2003).

Tao, T., "Nonlinear Dispersive Equations: Local and Global analysis", CBMS Conference Series (2006).