Restricted interpolation by meromorphic inner functions

Abstract

Meromorphic Inner Functions (MIFs) on the upper half plane play an important role in applications to spectral problems for differential operators. In this paper, we survey some recent results concerning function theoretic properties of MIFs and show their connections with spectral problems for the Schrödinger operator.

Uniqueness theorems for meromorphic inner functions and canonical systems

“…Existence, uniqueness, interpolation and other complex function theoretic problems for MIFs were recently studied in various papers [2,15,18,19]. In this paper we consider unique determination of the MIF Θ from several spectral data and conditions depending fully or partially on σ(Θ), σ(−Θ) and {µ Θ (t)} t∈σ(Θ) .…”