96756 - Advanced Mathematical Analysus

Learning outcomes

At the end of the course, students will possess the knowledge of the main instruments of advance mathematical analysis: Sobolev spaces, spaces of generalized functions, Fourier transform. These tools will be the main instruments necessary to the quantitative and qualitative study of properties of the solutions to PDEs.

Course contents

Metric spaces (with emphasis on completess) 

Measure theory

Hilbert space/Fourier series

Basic Functional Analysis

Readings/Bibliography

Lecture notes on Virtuale

Suggested reading:

Richard F. Bass, Real Analysis for Graduate Students Version 4.3, 2022 https://bass.math.uconn.edu/real.html

Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications 2nd Edition, Wiley 1999

Michael Reed, Barry Simon, Functional Analysis, 1981

Walter Rudin, Real and Complex Analysis, McGraw-Hill 1986

Terence Tao, An Introduction to Measure Theory, AMS 2011 https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf

Teaching methods

Lectures and exercise sessions.

Assessment methods

Written and oral exam.

A slightly different assessment method will be used for students who are especially active in their participation.

Teaching tools

Online tools and repository of course material.

Office hours

See the website of Nicola Arcozzi