The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912711891222528 |
|---|---|
| author | Matei-Luca, Marin |
| author_facet | Matei-Luca, Marin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09622 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators Matei-Luca, Marin Functional Analysis 47A60, 47B25, 26A39 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. |
| title | The Henstock-Kurzweil Functional Calculus on Self-Adjoint Operators |
| topic | Functional Analysis 47A60, 47B25, 26A39 |
| url | https://arxiv.org/abs/2510.09622 |