This course explores topics in measure theory and functional analysis. The topics covered in this course include: Lebesgue measure, Lebesgue integration, normed spaces, Banach spaces, Fourier series and wavelets, and Hilbert spaces, together with their applications. Additional topics may include Hahn-Banach theorem, bounded linear operators on Hilbert spaces, Riesz representation theorem, Sobolev spaces, and self-adjoint operators.
Prerequisites
MAT 570