Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.00669 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912357121261568 |
|---|---|
| author | Zhang, Ashley R. |
| author_facet | Zhang, Ashley R. |
| contents | This note focuses on the direct spectral problem for canonical Hamiltonian systems on the half-line $\mathbb{R}_+$. Truncated Toeplitz operators have been effectively used to solve the inverse spectral problem when the spectral measure is a locally finite periodic measure (see \cite{MP}). Here, we reverse the inverse problem algorithm to solve the direct spectral problem for step-function Hamiltonians. For a non-step-function Hamiltonian, we consider its step-function approximations and their corresponding spectral measures, and show that these spectral measures converge to the spectral measure of the original Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Direct spectral problems for Paley-Wiener canonical systems Zhang, Ashley R. Spectral Theory This note focuses on the direct spectral problem for canonical Hamiltonian systems on the half-line $\mathbb{R}_+$. Truncated Toeplitz operators have been effectively used to solve the inverse spectral problem when the spectral measure is a locally finite periodic measure (see \cite{MP}). Here, we reverse the inverse problem algorithm to solve the direct spectral problem for step-function Hamiltonians. For a non-step-function Hamiltonian, we consider its step-function approximations and their corresponding spectral measures, and show that these spectral measures converge to the spectral measure of the original Hamiltonian. |
| title | Direct spectral problems for Paley-Wiener canonical systems |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2505.00669 |