Uniqueness theorems for meromorphic inner functions and canonical systems
Abstract
We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum of the negative of a meromorphic inner function. Moreover we consider applications of these uniqueness results to inverse spectral theory of canonical Hamiltonian systems and obtain generalizations of Borg-Levinson two-spectra theorem for canonical Hamiltonian systems and unique determination of a Hamiltonian from its spectral measure under some conditions.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.12384
- arXiv:
- arXiv:2110.12384
- Bibcode:
- 2021arXiv211012384H
- Keywords:
-
- Mathematics - Complex Variables;
- 30;
- 34
- E-Print:
- A new section on applications to inverse spectral theory of canonical systems is added