Clark Measures for Rational Inner Functions

Conformal Measures for Rational Functions

We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism. 1 Introduction. In this paper we recall from U2] the...

Conformal measures for rational functions revisited

We show that the set of conical points of a rational function of the Riemann sphere supports at most one conformal measure. We then study the problem of existence of such measures and their ergodic properties by constructing Markov partitions on increasing subsets of sets of conical points and by applying ideas of the thermodynamic formalism. Introduction. In this paper we recall from [U2] the ...

Transfer Function Realization of Rational Inner Functions

My talk will be based on paper " Synthesis of two-dimensional loss-less m-ports with prescribed scattering matrix " by A. Kummert.

Algebraic and geometric aspects of rational Γ - inner functions

Abstract The set Γ def = {(z + w, zw) : |z| ≤ 1, |w| ≤ 1} ⊂ C has intriguing complex-geometric properties; it has a 3-parameter group of automorphisms, its distinguished boundary is a ruled surface homeomorphic to the Möbius band and it has a special subvariety which is the only complex geodesic that is invariant under all automorphisms. We exploit this geometry to develop an explicit and detai...

On the differential structure of matrix–valued rational inner functions