Nevanlinna - Pick Interpolation For

Ela Spectral versus Classical Nevanlinna-pick Interpolation in Dimension Two∗

A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.

Boundary Nevanlinna-Pick interpolation via reduction and augmentation

We give an elementary proof of Sarason’s solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The proofs are based on a reduction method due to Nevanlinna and the fact that reduction of functions corresponds to Schur complementation of the corresponding Pick...

Spectral versus classical Nevanlinna-Pick interpolation in dimension two

A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.

Nevanlinna-pick Interpolation on Distinguished Varieties in the Bidisk

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.

Nevanlinna-pick Interpolation: the Degenerated Case

. C V ] 2 2 Ju l 2 00 5 , BOUNDARY NEVANLINNA – PICK INTERPOLATION PROBLEMS FOR GENERALIZED SCHUR FUNCTIONS

is positive semidefinite for every choice of an integer n and of n points z1, . . . , zn ∈ D. The significance of this characterization for interpolation theory is that it gives the necessity part in the Nevanlinna-Pick interpolation theorem: given points z1, . . . , zn ∈ D and w1, . . . , wn ∈ C, there exists w ∈ S with w(zj) = wj for j = 1, . . . , n if and only if the associated Pick matrix ...