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Some Extensions of Loewner's Theory of Monotone Operator Functions

✍ Scribed by D. Alpay; V. Bolotnikov; A. Dijksma; J. Rovnyak

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
171 KB
Volume
189
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

to marvin rosenblum, with best wishes on the occasion of his retirement

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 o-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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