Course Descriptions

16:640:507 - Functional Analysis I

Denis Kriventsov

Text: 

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

Prerequisites:

16:640: 501 and 16:640:502

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.


Schedule of Sections: