Automorphic de Branges - Rovnyak Spaces

Abstract

A family of automorphic de Branges - Rovnyak spaces (depending on an arbitrary character $\alpha$) is associated to a $\beta$-automorphic analytic function $w$ bounded in modulus by $1$. Multiplication by the Green function defines unitary operators acting between those spaces. Function $w$ can be recovered from these operators as the characteristic function. It is shown that for Nevanlinna-Pick problem this family of unitary operators extends the family of isometric operators defined by the interpolation data.