Ratcliff, Gail Dawn LoraineChilcoat, Kenneth2016-05-262016-05-262016-052016-04-25May 2016http://hdl.handle.net/10342/5344The Spectral Theorem for Self-Adjoint Operators allows one to define what it means to evaluate a function on the operator for a large class of functions defined on the spectrum of the operator. This is done by developing a functional calculus that extends the intuitive notion of evaluating a polynomial on an operator. The Spectral Theorem is fundamentally important to operator theory and has applications in many fields, especially harmonic analysis on locally compact abelian groups. This thesis represents a merging of two traditional treatments of the Spectral Theorem and includes an extended example highlighting an important application in harmonic analysis.application/pdfenHilbert SpaceSpectral theory (Mathematics)Operator theoryHarmonic analysisMaster's Thesis2016-05-25