The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators

Abstract

This dissertation focuses on developing a new construction of a functional calculus using Henstock-Kurzweil integration methods. The assignment of a functional calculus will be applied to self-adjoint operators. We will address both the bounded and unbounded cases, examine the advantage of the underlying function space compared to larger spaces, prove the spectral mapping theorem, and explore one application of this functional calculus in abstract differential equations.