Functional Analysis

1 Course Unit

Convexity and the Hahn Banach Theorem. Hilbert Spaces, Banach Spaces, and examples: Sobolev spaces, Holder spaces. The uniform bounded principle, Baire category theorem, bounded operators, open mapping theorem, closed graph theorem and applications. The concepts of duality and dual spaces. The Riesz theory of compact operators and Fredholm theory. Functional calculus and elementary Spectral Theory. Interpolation theorems. Applications to partial differential equations and approximation theory. Prerequisite: MATH 6080 OR MATH 6090 1 Course Unit