# MATH 565 Introduction to Spectral Theory

Hilbert spaces. Spectral theory in finite dimensional spaces. Spectral properties of bounded and compact linear operators. Spectral theorem of bounded normal operators. Spectral representation of bounded self-adjoint operators. Unbounded linear operators and their adjoints. Closed operators. Spectral representation of unitary operators. Spectral representation of unbounded self-adjoint operators. Regular Sturm-Liouville operators. Linear operators in quantum mechanics.