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Abstract In this note, we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second‐order differential equations on a half‐line. Our goal is to extend the classical results developed in the work of Marchenko, Gelfand–Levitan, and Krein to broader classes of canonical systems and to illustrate the solution algorithms and formulae with a variety of examples. One of the main ingredients of our approach is the use of truncated Toeplitz operators, which complement the standard toolbox of the Krein–de Branges theory of canonical systems.
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This content will become publicly available on March 1, 2026
Uniqueness theorems for meromorphic inner functions and canonical systems
Abstract We consider 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 the Borg-Levinson two-spectra theorem for canonical Hamiltonian systems and unique determination of a Hamiltonian from its spectral measure under some conditions.
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- Award ID(s):
- 2052519
- PAR ID:
- 10617156
- Publisher / Repository:
- Cambridge Core
- Date Published:
- Journal Name:
- Canadian Mathematical Bulletin
- Volume:
- 68
- Issue:
- 1
- ISSN:
- 0008-4395
- Page Range / eLocation ID:
- 124 to 140
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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