Some Extensions of Loewner's Theory of Monotone Operator Functions

Some Extensions of Loewner's Theory of Monotone Operator Functions

Several extensions of Loewner's theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalar-to matrix-valued functions of...

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Bibliographic Details
Published in:Journal of functional analysis Vol. 189; no. 1; pp. 1 - 20
Main Authors: Alpay, D., Bolotnikov, V., Dijksma, A., Rovnyak, J.
Format: Journal Article
Language:English
Published: Elsevier Inc 20-02-2002
Online Access:Get full text
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Summary:Several extensions of Loewner's theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalar-to matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical Nevanlinna functions with removable singularities on a real interval. Corresponding results for Stieltjes functions are presented.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.2001.3856