28393 - Functional Analysis 1

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of the course, the student has basic skills in Functional Analysis and in the theory of Linear Operators. He/she knows how to exploit this knowledge to solve problems in some Differential Equations of Mathematical Physics.

Course contents

Functional Analysis deals with infinite dimensional spaces and operators acting on them. It has both a theoretic and an applied nature: it has its own "axiomatic" body of knowledge, but it lives of applications. The course will cover:

Hilbert and Banach spaces;

Bounded Operators on such spaces, and spaces of such operators;

Spectral Theory for Bounded Operators;

Spectral Theory for Unbounded Operators.

Applications to Physiscs, Partial Differential Equations, Signal Theory, etcetera, will be discussed. The choice of the applications will be decided during the class, keeping into account the interests of the students and of the instructor.

Readings/Bibliography

Michael Reed and Berry Simon; Methods of Modern Mathematical Physics, Volume I: Functional Analysis; Academic Press; 1972

Peter Lax; Functional Analysis Wiley-Interscience; 2002

Teaching methods

Lectures and some exercise sessions.

Assessment methods

Some exercises will be given during the class. Exercises and theory will be discussed during an oral exam. Students are encouraged to deliver a seminar during the class. The seminar will be evaluated in the final grade.

Teaching tools

Some material will be made available online.

Office hours

See the website of Nicola Arcozzi