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Boundary Nevanlinna–Pick interpolation for Nevanlinna matrix functions and the related Hamburger matrix moment problem
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Yong-Jian Hu
Published/Copyright:
September 25, 2009
Abstract
This paper is concerned with a boundary Nevanlinna–Pick interpolation for Nevanlinna matrix functions and the Hamburger matrix moment problem but with specified constraints that the nonnegative matrix-valued measure has no mass distributions at a finite number of real points. Intrinsic connections between these two problems are established by the so-called Hankel vector approach. The connections, together with the theory of matrix moments and the theory of matrix polynomials with respect to a positive Hermitian block Hankel matrix due to H. Dym, enable us to get a solvability criterion and a parameterized description of all the solutions for each of these two problems.
Keywords: Boundary Nevanlinna-Pick interpolation; Nevanlinna matrix function; Hamburger matrix moment problem; nonnegative matrix-valued measure; block Pick matrix
Published Online: 2009-09-25
Published in Print: 2009-04
© by Oldenbourg Wissenschaftsverlag, München, Germany
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Articles in the same Issue
- Restrictions of power series and functions to algebraic surfaces
- Approximate continuity and topological Boolean algebras
- A Tauberian theorem for absolute quasi-Nörlund means
- Boundary Nevanlinna–Pick interpolation for Nevanlinna matrix functions and the related Hamburger matrix moment problem
- Some new results on the semiduality of small sets of analytic functions
- A note on globally defined analytic sets
- Counterexamples to symmetry for partially overdetermined elliptic problems
- A uniqueness-type problem for linear iterative equations
- A new bound of Mason´s theorem
