MA559
Orthogonal Systems
0.5 Credit

This course studies orthogonal systems of functions related to ordinary and partial differential equations. Topics include: inner product spaces; Hilbert spaces; Hermitian and self-adjoint linear operators; Sturm-Liouville theory; generating functions and orthogonal polynomials; Green's functions; completeness and over-completeness; eigenfunction expansions in one and several variables; infinite and semi-infinite orthonormal bases. Applications include solution methods for parabolic partial differential equations, Fourier series, wavelets, wavelet transforms, and other expansion methods. Topics may include integral representations and transforms, spectral theory, point-wise convergence and convergence in the norm.