Pick interpolation for a uniform algebra

Nevanlinna - Pick Interpolation For

We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...

Nevanlinna-pick Interpolation for C + Bh ∞

In this paper we will consider the Nevanlinna-Pick problem for a class of subalgebras of H∞. Let us assume that we are given n points z1, . . . , zn ∈ D, n complex numbers w1, . . . , wn and a subalgebra A of H ∞. We will say that a function f ∈ A, interpolates the values z1, . . . , zn to w1, . . . , wn if and only if ‖f‖∞ ≤ 1 and f(zj) = wj . Such an f will be called an interpolating function...

Pick Interpolation for free holomorphic functions

A Constrained Nevanlinna-pick Interpolation Problem

We obtain necessary and sufficient conditions for NevanlinnaPick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy f ′(0) = 0. Alternatively, these results can be interpreted as interpolation results for H∞(V ), where V is the intersection of the bidisk with an algebraic variety. We use an analysis of C*-envelopes to show that these...

Parametric Nevanlinna-Pick Interpolation Theory

We consider the robust control problem for the system with real uncertainty. This type of problem can be represented with some parameters varying between the boundaries and is formulated as parametric Nevanlinna-Pick interpolation problem in this paper. The existence of a solution for such interpolation problem depends on the positivity of the corresponding Pick matrix with elements belonging t...