Abstract
In this chapter we study a variant of the Nevanlinna-Pick interpolation problem where one seeks a function analytic and bounded by 1 on a domain which meets a set of interpolation conditions, some of which may now be prescribed on the boundary of the domain. When the interpolation conditions are of a suitable form, it develops that the set of all solutions is parametrized by a linear fractional map induced by a J-inner function having poles on the boundary, a phenomenon originally observed by Nevanlinna. Matrix extensions of this result provide an area of application for results in Chapters 6 and 7 concerning the structure of such J-inner functions, and form a natural extension of the results of Chapters 18 and 19 to the boundary case. This boundary interpolation is also sometimes called Loewner interpolation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes for Part V
J.A. Ball and J.W. Helton [ 1986b ], Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: parametrization of the set of all solutions, Integral Equations and Operator Theory 9, 155–203.
P. Dewilde and H. Dym [ 1984 ], Lossless inverse scattering for digital filters, IEEE Trans. Information Theory 30, 644–662.
J.A. Ball [ 1983 ], Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions, Integral Equations and Operator Theory 6, 804–840.
M. Rosenblum and J. Rovnyak [ 1985 ], Hardy Classes and Operator Theory, Oxford University Press, New York.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Basel AG
About this chapter
Cite this chapter
Ball, J.A., Gohberg, I., Rodman, L. (1990). Boundary Nevanlinna-Pick Interpolation. In: Interpolation of Rational Matrix Functions. Operator Theory: Advances and Applications, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7709-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7709-1_22
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7711-4
Online ISBN: 978-3-0348-7709-1
eBook Packages: Springer Book Archive