We prove some 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

Hatinoğlu, Burak

English

arXiv

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.Comment: A new section on applications to inverse spectral theory of canonical
  systems is adde

Uniqueness theorems for meromorphic inner functions

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