## MATH 806 - Fall
2015

**Official course description.**Fundamental results for normed linear spaces with special emphasis on the theory of Hilbert space, spectral theorems and application to integral and differential equations.

**My view.**We will explore the construction and properties of the most basic classes of functions spaces (normed spaces, Banach spaces, Hilbert spaces) and the operators defined between them. Most of the course will be focused on linear functional analysis. We will spend an important amount of time understanding the big theorems on Banach spaces while you (the students) explore the rudiments of Hilbert space theory. Then we will have a good look at the solvability theory and the spectral theory for compact operators in Hilbert space. Time permitting, we will try to fly high and have a look at algebras of operators.

**Basic data.**

- Lectures: MW 5:00 PM to 6:15 PM at Ewing 203
- Instructor: Francisco-Javier Sayas (www.math.udel.edu/~fjsayas)

- Textbook: Alberto Bressan.
*Lecture Notes on Functional Analysis.*AMS Graduate Studies in Mathematics, Volume 143. - Office hours: By appointment (see next item).
- Problem solving sessions: Mondays 1pm-2pm in
EWG336. Fridays 11am-noon in EWG336. These are to
be understood as group office hours, or
(equivalently) as tutored working time.

- Website: www.math.udel.edu/~fjsayas/teaching/math806