Functional analysis and applications: Math 797FN

Meeting : TuTh 9:30--10:45    LGRT 1234

Instructor : Luc Rey-Bellet

 Office :   1423 J LGRT
 Phone :  545-6020
 E-Mail :
 Office Hours :   Tu 11:00--12:00,   Th 3:00--4:00,   or by appointment.

Classnotesand homework: Some (partial) classnotes will be posted and regularly updated HERE

References: I will not follow any textbook very closely. You are however very strongly encouraged to consult textbooks on your own. There are dozens of books on functional analysis with the authors taking many different point of view. The books selected below are all in the same spirit as the class (or vice-versa).

Syllabus: 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. We will review these topics but at a rather brisk pace. 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

Grade: Homework will be assigned on a regular basis. Each student will pick a project of his choice. I expect a written project at the end of the semester and each student will give an oral presentation to the class.