Some extensions of Loewner's theory of monotone operator functions

摘要

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 kappa-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. (C) 2002 Elsevier Science (USA). [References: 20]