Some extensions of Loewner's theory of monotone operator functions

D. Alpay; V. Bolotnikov; A. Dijksma; J. Rovnyak

doi:10.1006/jfan.2001.3856

Some extensions of Loewner's theory of monotone operator functions

D. Alpay
, V. Bolotnikov
, A. Dijksma
, J. Rovnyak

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Journal of Functional Analysis
Volume	189
Issue number	1
DOIs	https://doi.org/10.1006/jfan.2001.3856
State	Published - 20 Feb 2002

ASJC Scopus subject areas

Analysis

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AB - 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.

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Some extensions of Loewner's theory of monotone operator functions

Abstract

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