16:640:507 Functional Analysis I

Fall 2019

Denis Kriventsov

Course Description:

Sobolev spaces and the variational formulation of boundary value problems in one dimension. The Hahn-Banach theorems. Conjugate convex functions. The uniform boundedness principle and the closed graph theorem. Characterization of surjective operators. Weak topologies. Reflexive spaces. Separable spaces. Uniform convexity. L^{p} spaces. Hilbert spaces. Compact operators. Spectral decomposition of self-adjoint compact operators.

Textbook:

Haim Brezis, "Functional Analysis, Sobolev Spaces, and Partial Differential Equations."

Prerequisites:

501 + 502