TOPICS IN ADVANCED ANALYSIS B

Degree course: 
Academic year when starting the degree: 
2015/2016
Year: 
2
Academic year in which the course will be held: 
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

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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