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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| Vydané v: | Journal of functional analysis Ročník 189; číslo 1; s. 1 - 20 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Inc
20.02.2002
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| ISSN: | 0022-1236, 1096-0783 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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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| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1006/jfan.2001.3856 |