Tangential interpolation problems for a class of automorphic matrix-functions
Copyright policy )Tangential interpolation problems for a class of automorphic matrix-functions
The authors consider an interpolation problem called the \((A,B,C)\)-problem (see \textit{A. A. Nudel'man} [Sov. Math., Dokl. 18, 507--510 (1977); translation from Dokl. Akad. Nauk SSSR 233, 792--795 (1977; Zbl 0372.30039); Oper. Theory, Adv. Appl. 61, 171--188 (1993; Zbl 0796.47007)] for details) in the class \((R)_\Gamma\), consisting of matrix-valued functions in Nevanlinna clas \((R)\) which are invariant under some fixed linear fractional transformation \(\Gamma\) of the upper half-plane into itself. They develop an abstract scheme of the problem and give a formula for the description of all invariant solutions of the abstract problem in the completely indeterminate case. They also show that the abstract scheme works for the case of the \((A,B,C)\)-problem, which generalizes the classical Nevanlinna--Pick problem.
- Odessa National Academy of Food Technologies Ukraine
- Missouri University of Science and Technology United States
linear fractional transformation, Nevanlinna--Pick problem, Numerical Analysis, Algebra and Number Theory, Interpolation problem, interpolation problem, Linear fractional transformation, Automorphic function, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), automorphic function, \((A,B,C)\)-problem, Nevanlinna class, Discrete Mathematics and Combinatorics, Geometry and Topology, Linear operator methods in interpolation, moment and extension problems
linear fractional transformation, Nevanlinna--Pick problem, Numerical Analysis, Algebra and Number Theory, Interpolation problem, interpolation problem, Linear fractional transformation, Automorphic function, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), automorphic function, \((A,B,C)\)-problem, Nevanlinna class, Discrete Mathematics and Combinatorics, Geometry and Topology, Linear operator methods in interpolation, moment and extension problems
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