Poll

No polls currently selected on this page!

Repository

Repository is empty

Harmonic analysis

Code: 61473
ECTS: 5.0
Lecturers in charge: izv. prof. dr. sc. Vjekoslav Kovač - Lectures
Lecturers: Aleksandar Bulj, mag. math. - Exercises
Load:

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 15
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: It serves as an introduction to one of the important subjects in modern analysis, it is also a continuation of the course on Fourier series.

COURSE DESCRIPTION AND SYLLABUS:
1. Summary of Fourier series.
2. Poisson integral and Riesz theorem.
3. Hardy-Littlewood maximal function.
4. Riesz - Thorin theorem.
5. Hausdorff - Young theorem.
6. Fourier transform on L1(R).
7. Parseval formula and applications.
8. Bochner theorem.
9. Fourier transform on Lp(R), 1 10.Tempered distributions.
11. Distributions.
12. Paley - Wiener theorem.

TEACHING AND ASSESSMENT METHODS:
Lectures and exercise sections. Regular attendance is required, and there will be homeworks and tests administered in the classroom.

PREREQUISITES: Fourier series and applications
Literature:
  1. A. Deitmar: A First Course in Harmonic Analysis
  2. Y. Katznelson: An Introduction to Harmonic Analysis
  3. W. Rudin: Fourier Analysis on Groups
  4. E. Stein, G. Weiss: Introduction to Fourier Analysis on Euclidean Spaces
3. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

4. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics
Consultations schedule: