Some Extensions of Loewner's Theory of Monotone Operator Functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Some Extensions of Loewner's Theory of Monotone Operator Functions

Authors:	D AlpayV Bolotnikov A DijksmaJ Rovnyak

Institution:	^a Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israelf1E-mail: dany@ivory.bgu.ac.ilf1 ^b Department of Mathematics, College William and Mary, Williamsburg, Virginia, 23187-8795, f2E-mail: vladi@math.wm.eduf2 ^c Department of Mathematics, University of Groningen, P.O. Box 800, 9700, AV Groningen, The Netherlandsf3E-mail: dijksma@math.rug.nlf3 ^d Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, Virginia, 22904-4137, f4E-mail: rovnyak@Virginia.eduf4

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.

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