**University of Utah - Department of
Mathematics
MATH 7280 **

**
Instructo**r: Marian BOCEA

**Homework Assignments:**

Homework
# 1 (due February 17, 2006, at
the end of the lecture)

Homework
# 2 (due March
27, 2006, at
the end of the lecture)

Homework # 3 (due April 24, 2006, at the end of the lecture)

**Office**: JWB 203

**Phone**: (801)585-6967

**E-mail**: bocea@math.utah.edu

**Class meets**: MWF 2:00 PM-2:50 PM.* Room: *JTB
110

**Text**: We will use selected chapters from the following
books:

1. H. BREZIS, Analyse fonctionnelle. Theorie et Applications.*
Dunod, Paris*, 1999

2. P. LAX, Functional Analysis. *Wiley*, 2002

3. F. HIRSCH and G. LACOMBE, Elements of Functional Analysis. *Springer*,
1999

4. R.E. EDWARDS, Functional Analysis: Theory and Applications. *Dover*,
1999

**Course Web Page**:
http://www.math.utah.edu/~bocea/spring2006.html

**Prerequisites**: MATH 6210 Real Analysis, MATH 6220 Complex
Analysis, or consent of instructor.

**
Course Audience: **Graduate students interested in
Functional Analysis and its applications.

1. The Hahn-Banach theorem. Extensions of linear forms and separation of convex sets.

2. The Banach-Steinhaus, closed graph, and open mapping theorems. Unbounded operators, adjoint, the characterization of surjective operators.

3. Weak topologies. Reflexive, separable, and uniform convex spaces.

4. L^{p} spaces. Reflexivity, separability, duals, convolution and regularization.

5. Hilbert spaces. The theorems of Stampacchia and Lax-Milgram.

6. Compact operators. Spectral decomposition of selfadjoint compact operators. Riesz-Fredholm theory.

7. The Hille-Yoshida theorem. Maximal monotone operators.

8. The theory of distributions and Sobolev spaces. The variational formulation of boundary value problems for PDEs.

There will be a take home Final Exam. Details will be available on the web site of the course after April 15, 2006.

Grading:

Your final grade for the course will be determined as follows: Homework Average: 50%. Final Exam: 50%.