 

Joseph A. Ball and Vladimir Bolotnikov
NevanlinnaPick interpolation for SchurAgler class functions on domains with matrix polynomial defining function in C^{n}


Published: 
June 22, 2005 
Keywords: 
Operator valued functions, SchurAgler class, NevanlinnaPick interpolation 
Subject: 
47A57 


Abstract
We consider a bitangential interpolation problem for operatorvalued
functions defined on a general class of domains in C^{n} (including
as particular cases, Cartan domains of types I, II and
III) which satisfy a type of von Neumann inequality
associated with the domain.
The compact formulation of the
interpolation conditions via a functional calculus with
operator argument includes prescription of various combinations of
functional values and of higherorder partial derivatives along
left or right directions at a prescribed subset of the domain as
particular examples.
Using realization results for such functions
in terms of unitary colligation and the defining polynomial for the
domain, necessary and sufficient conditions for the problem to have a
solution were established recently in Ambrozie and Eschmeier (preprint, 2002),
and Ball and Bolotnikov, 2004.
In this paper we present a parametrization of the set of all solutions in
terms of a Redheffer linear fractional transformation acting on a
freeparameter function from the class subject to no interpolation
conditions. In the finitedimensional case
when functions are matrixvalued, the matrix of the linear fractional
transformation is given explicitly in terms of the interpolation data.


Author information
Joseph A. Ball:
Department of Mathematics, Virginia Polytechnic Institute, Blacksburg, VA 240610123, USA
ball@calvin.math.vt.edu
Vladimir Bolotnikov:
Department of Mathematics, The College of William and Mary, Williamsburg VA 231878795, USA
vladi@math.wm.edu

