UC Davis Math 202
Functional Analysis

Basic information

SYLLABUS

Grading:

Reading:

Graduate Studies in Mathematics, 66. American Mathematical Society, Providence, RI, 2004. available on Amazon

Lectures

Lecture 1 (January 7): Introduction. Baire Category Theorem.

Lecture 2 (January 9): Baire Category Theorem (cont).

Lecture 3 (January 11): Open Mapping Theorem. Equivalent norms on a Banach space.

Lecture 4 (January 14): Closed Graph Theorem.

Lecture 5 (January 16): Closed Graph Theorem (cont). Hoermander's bound on the sup-norm of the derivative.

Lecture 6 (January 23): Banach-Steinhaus Theorem.

Lecture 7 (January 25): Applications of Banach-Steinhaus Theorem.

Lecture 8: (January 28): Linear Functionals. Hahn-Banach theorem.

Lecture 9 (January 30): Linear Functionals. Hahn-Banach theorem. Applications.

Lecture 10 (February 1): Bases in Banach spaces.

Lecture 11 (February 4): Separation of Convex Sets.

Lecture 12 (February 6): Separation of Convex Sets. Minkowski Functional.

Lecture 13 (February 8): Review.

Lecture 14 (February 13): Spectrum. Classification of Spectrum.

Lecture 15 (February 15): Spectrum. Compact Linear Operators.

Lecture 16 (February 20): Fredholm Theory of Compact Operators.

Lecture 17 (February 22): Fredholm Theory of Compact Operators (cntd).

Lecture 18 (February 25): Self-Adjoint Operators

Lecture 19 (February 27): Integral Operators

Lecture 20 (March 1): Minimax Principle

Homework, Midterm, and Final Exam.

Homework 1

(assigned on January 25):

Homework 2

(assigned on February 1):

Midterm

(due in class on February 15):

Homework 3

(assigned on February 22):

Homework 4

(assigned on March 1): 6.4.10-6.4.13, 6.5.1-6.5.5

Final Exam

(due March 21 by 1pm):