The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators
Functional Analysis
2025-11-18 v3
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.
Cite
@article{arxiv.2510.09622,
title = {The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators},
author = {Marin Matei-Luca},
journal= {arXiv preprint arXiv:2510.09622},
year = {2025}
}
Comments
73 pages. This replacement fixes some typos from the previous version of the proof of the Spectral Mapping Theorem