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 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).</p

Some Extensions of Loewner\u27s 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 an operator argument. A notion of -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

Notes on Interpolation in the Generalized Schur Class. II. Nudelman\u27s Problem

An indefinite generalization of Nudel′man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for Pick-Nevanlinna and Carath´eodory-Fej´er interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel′man’s problem

On Nudel'man's Problem and Indefinite Interpolation in the Generalized Schur and Nevanlinna Classes

This work is a revised and corrected version of the authors' joint paper with T. Constantinescu (Trans Am Math Soc 355:813-836, 2003). Some of the theorems from the original paper that are withdrawn are recast as new open problems for indefinite interpolation. Partial results are obtained by other methods, including Kronecker's theorem for Hankel operators

On Nudel’man’s Problem and Indefinite Interpolation in the Generalized Schur and Nevanlinna Classes

This work is a revised and corrected version of the authors’ joint paper with T. Constantinescu (Trans Am Math Soc 355:813–836, 2003). Some of the theorems from the original paper that are withdrawn are recast as new open problems for indefinite interpolation. Partial results are obtained by other methods, including Kronecker’s theorem for Hankel operators