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arXiv · 2110.12384

Uniqueness theorems for meromorphic inner functions and canonical systems

Burak Hatinoğlu
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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.

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Burak Hatinoğlu. 2021-10-24. Uniqueness theorems for meromorphic inner functions and canonical systems. https://doi.org/10.4153/s0008439524000614

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