TOPICS IN ADVANCED ANALYSIS A

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academyc year when starting the degree: 
2017/2018
Year: 
1
Academyc year when helding the course: 
2017/2018
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

Oral exam with a term paper on a chosen topic. The precise modality of the exam will be discussed with the student.

Assessment: 
Voto Finale

Introduction to Commutative Harmonic Analysis on R^n

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

References to texts will be given at the beginning of the course

Lectures

Professors

Borrowers