Course Descriptions

16:640:507 - Functional Analysis I

Fioralba Cakoni

Text: 

Haim Brezis "Functional Analysis, Soblolev Spaces and PDE's" Springer

Prerequisites:

Real Analysis I and II

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: