1. komponenta

Lecture type	Total
Lectures	30
Exercises	15

* Load is given in academic hour (1 academic hour = 45 minutes)

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

1. A First Course in Harmonic Analysis, A. Deitmar, Springer Verlag, 2002.
2. An Introduction to Harmonic Analysis, Y. Katznelson, Dover, 1976.
3. Fourier Analysis on Groups, W. Rudin, Interscience, 1962.
4. Introduction to Fourier Analysis on Euclidean Spaces, E. Stein, G. Weiss, Princeton University Press, 1971.

Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

Izborni predmet 3, 4 - Regular study - Theoretical Mathematics