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Math 725 - Functional Analysis

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Spring 2020

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Prof. Andrea R.
Nahmod

**Office****: LGRT 1540 **

Tel : (413) 545 6031

Email :
mylastname at math dot umass dot edu

Prerequisites: M623 and M624

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

**Description:
**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.

Textbook 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.

__Some
Handouts:__

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### Grading Policy:* *Grade
determined by class participation (__attendance for
this class is mandatory__), class presentations and
and fulfillment of homework assignments.

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