Geodesic
Uniqueness theorems for meromorphic inner functions and canonical systems
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 124-140

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DOI

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.
DOI : 10.4153/S0008439524000614
Mots-clés : meromorphic inner functions, uniqueness theorems, canonical Hamiltonian systems, inverse spectral theory, Weyl m-functions 
Hatinoğlu, Burak. Uniqueness theorems for meromorphic inner functions and canonical systems. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 124-140. doi: 10.4153/S0008439524000614
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     title = {Uniqueness theorems for meromorphic inner functions and canonical systems},
     journal = {Canadian mathematical bulletin},
     pages = {124--140},
     year = {2025},
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     doi = {10.4153/S0008439524000614},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000614/}
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