Real Analysis II

3 credits · Graduate credit

Spaces of continuous functions: Stone-Weierstrass and Arzela-Ascoli theorems; Hilbert spaces: projections, orthonormal systems, Parseval's identity, linear functionals; Banach spaces: principle of uniform boundedness, closed graph theorem, Hahn-Banach theorem, Riesz representation theorem; Fourier series and integrals; Sobolev spaces; Hausdorff measure and dimension.