Math 725 - Functional Analysis

                                                           Spring 2020

                                                Prof.  Andrea R. Nahmod

Office: LGRT 1540
(413) 545 6031

:  mylastname at math dot umass dot edu 

  M623 and M624

Meeting Times
Tuesdays and Thursdays  2:30am - 3:45pm in LGRT 1114

Functional analysis deals with the structure of infinite dimensional vector spaces and (mostly) linear on such spaces. Many such spaces are spaces of functions, hence the name functional analysis, but much of the theory will developed for abstract spaces (spaces with a norm or a scale product). We shall assume that the reader has taken Math 624 (or an equivalent course) and is familiar with the basic objects of functional analysis: Banach spaces and Hilbert spaces, linear functionals and duals, bounded linear operators. Our main goal is to develop a series of tools instrumental in the applications of functional analysis to PDE's, probability, ergodic theory, etc... Among the topics covered in this class are:  Hahn-Banach theorem, Inverse mapping and closed graph theorems. Compact operators, Fredholm operators and applications; Spectral theory for linear bounded and unbounded operators, Banach algebras, Semigroups. Time permitting we will also cover the theory of distributions and Sobolev spaces.

  Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis; Universitext- Springer (2011).

Reference Book (optional)  I: Functional Analysis (Methods of Modern Mathematical Physics) by M. Reed and B. Simon. Revised and Enlarged Edition Elsevier Science Ed.

Homeworks (click here)

Some Handouts:

Grading Policy: Grade determined by class participation (attendance for this class is mandatory), class presentations and and fulfillment of  homework assignments.