TOPICS IN ADVANCED ANALYSIS A
Lebesgue integral, basic Functional Analysis, Lp spaces, basic Probability Theory
Oral exam with a term paper on a chosen topic. The precise modality of the exam will be discussed with the student.
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