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
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