TOPICS IN ADVANCED ANALYSIS B

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academyc year when starting the degree: 
2016/2017
Year: 
1
Academyc year when helding the course: 
2016/2017
Course type: 
Compulsory subjects, characteristic of the class
Credits: 
8
Period: 
First Semester
Standard lectures hours: 
80
Detail of lecture’s hours: 
Lesson (80 hours)
Requirements: 

Lebesgue integral, basic Functional Analysis, Lp spaces, basic Probability Theory

Final Examination: 
Orale
Assessment: 
Voto Finale

Tools and concepts of Abelian Harmonic Analysis

Fourier Series and Integrals
Harmonic Functions and the Poisson Kernel
Conjugate Harmonic Functions nd the Hilbert Transform.
Fourier Transforms in the space Rn.
Recall of some notions of Probability Theory.
Random Fourier Seriese.
Introduction to Singular Integrals and the Calderon-Zygmund Theory

C. Muscalu, W. Schlag, Classical and Multilinear Harmonic Analysis, vol 1.

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