Introduction to Harmonic Analysis

First lecture:
Wednesday, February 18.

Course attendance confirmation (Testat) requirements:
No.

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, Littlewood-Paley theory, and Oscillatory integrals. In the end of the course, we will give an application to the theory to the study of dispersive partial differential equations.

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 will be provided during the course of the semester.

Assignments

There will be several assignments which are not meant to be turned in. They will be helpful to prepare for the oral exam.

References

• 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).