January 28, 2008
Aad Dijksma
Title: The Schur transformation for Nevanlinna functions: operator representations, resolvent matrices, and orthogonal polynomials
We consider a fractional linear transformation for a Nevanlinna function $n$ with a suitable asymptotic expansion at $\infty$, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation $p$ times we find a Nevanlinna function $n_p$ which is a fractional linear transformation of the given function $n$. We discuss the effect of this transformation to the realizations of $n$ and $n_p$, by which we mean their representations through resolvents of self-adjoint operators in Hilbert space. The lecture is based on joint work with Daniel Alpay (Beer Sheva) and Heinz Langer (Vienna).