Uniqueness results for meromorphic inner functions

Analysis Seminar
Wednesday, March 8, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005
Burak Hatinoglu – Georgia Tech – bhatinoglu3@gatech.edu
Benjamin Jaye

A meromorphic inner function is a bounded analytic function on the upper half plane with unit modulus almost everywhere on the real line and a meromorphic continuation to the complex plane. Meromorphic inner functions and equivalently meromorphic Herglotz functions play a central role in inverse spectral theory of differential operators. In this talk, I will discuss some uniqueness problems for meromorphic inner functions and their applications to inverse spectral theory of canonical Hamiltonian systems as Borg-Marchenko type results.