@article{12baf54a526e4f97915b2663fe73d247,

title = "Some extensions of Loewner's theory of monotone operator functions",

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.",

author = "D. Alpay and V. Bolotnikov and A. Dijksma and J. Rovnyak",

note = "Funding Information: Several extensions of Loewner{\textquoteright}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. {\textcopyright} 2002 Elsevier Science (USA) 1A. Dijksma was supported by a Harry T. Dozor fellowship at the Ben-Gurion University of the Negev, Beer-Sheva, Israel. J. Rovnyak was supported by the National Science Foundation Grant DMS–9801016.",

year = "2002",

month = feb,

day = "20",

doi = "10.1006/jfan.2001.3856",

language = "English",

volume = "189",

pages = "1--20",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "1",

}