Michael Papadimitrakis

Department of Mathematics and Applied Mathematics, University of Crete

Voutes campus, 70013 Heraklion

Office: Γ 211

E-mail: mpapadim@uoc.gr, mihalis.papadimitrakis@gmail.com

Telephone: 2810393840

Personal webpage

Spring 2023-24

Harmonic Analysis (advanced graduate)

Περιεχόμενα

• 1 Preliminaries.
  • 1.1 Content of the course.
  • 1.2 Lectures.
  • 1.3 Required knowledge.
  • 1.4 Bibliography.
  • 1.5 Evaluation.
  
  
• 2 Calendar.

1 Preliminaries.

1.1 Content of the course.

The Fourier transform in L1.

The Fourier transform in L2.

The Fourier transform in Lp, 1<p<2.

The Fourier transform in the space of complex measures.

The Fourier transform in the space of tempered distributions.

Depending on the time left, I plan to touch some of the following extra subjects: Bochner's theorem for positive definite distributions, the Paley-Wiener theorem for distributions of compact support, the uncertainty principle, Sobolev spaces, singular integrals (e.g. the Hilbert transform and the relation to Complex Analysis), the space of functions of bounded mean oscillation, etc.

1.2 Lectures.

11-13 every Monday and Wednesday in B214.

1.3 Required knowledge.

Very good knowledge of the graduate Real Analysis. The undergraduate Harmonic Analysis is not required.

1.4 Bibliography.

I shall follow personal (rough) notes.

Some very good books are: Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss, Lectures on Harmonic Analysis by Wolff, Functional Analysis by Yosida, Methods of Modern Mathematical Physics by Reed and Simon, Fourier Analysis by Duoandikoetxea. There are many many more!!

1.5 Evaluation.

Since the course is advanced, probably there will be no final exam. During the semester I shall assign exercises and you will have to give me the solutions of some of them (but solve all of them!).

2 Calendar.

Here I shall announce anything related to the course (notes, time changes, extra lectures, exercises etc.).

[13/2] The things I covered yesterday are here.

Tomorrow I shall continue the lectures in English since one of the students -poor fellow- is not Greek.

[15/2] The new notes. They contain everything I have covered so far (plus a few innocent corollaries).

[20/2] The latest notes.

If any student from Thessaloniki has any questions on the mathematics in my notes (or on my blackboard) we may arrange to talk via zoom or skype. Also note that I plan to be in Thessaloniki during 1-11 of March.

[22/2] The latest notes.