Math 567 Fall 2021 | Tsogtgerel Gantumur

Course Record

Graduate functional analysis course covering Banach and Hilbert spaces, weak convergence, compact operators, Fredholm theory, and spectral theory.

The recovered archive includes a full topic schedule, planned topics, recommended books, and the assessment structure.

Date	Topic
R 9/2	Introduction. Weierstrass existence theorem.
T 9/7	Finite dimensional spaces. Riesz lemma. Uniform convexity.
R 9/9	Hilbert spaces. Projection. Riesz representation.
T 9/14	Sobolev spaces. Strong derivatives.
R 9/16	Mollifiers. Du Bois-Reymond lemma. Weak derivatives.
T 9/21	Meyers-Serrin theorem. Sobolev lemma. Regularity.
R 9/23	Neumann problems. Rellich lemma. Complex scalars.
T 9/28	Orthonormal bases.
R 9/30	Fourier bases.
T 10/5	Sturm-Liouville problems. Resolvent formalism.
R 10/7	Hilbert-Schmidt theory.
F 10/15	Gelfand triples. Singular Sturm-Liouville problems.
T 10/19	Functional calculus. Evolution equations.
R 10/21	Seminorms. Local spaces. Tempered distributions.
T 10/26	Hahn-Banach theorem.
R 10/28	Milman-Pettis theorem.
T 11/2	Weak convergence. Uniform boundedness principle.
R 11/4	Banach-Alaoglu theorem.
T 11/9	Tychonov's theorem. Consequences of the open mapping theorem.
R 11/11	Open mapping theorem. Bounded below property. Range closedness.
T 11/16	Closed range theorem.
R 11/18	Inf-sup conditions. Saddle point problems.
T 11/23	Perturbations of invertible operators. Fredholm alternative.
R 11/25	Compact operators.
T 11/30	Riesz-Schauder theory. Fredholm operators. Regularizers.
R 12/2	Perturbations of Fredholm operators. Bounded self-adjoint operators.

The public archive records the schedule and course structure; course-management homework files are not included.