Additional Affiliations
Mathematics
Document Type
Article
Publication Date
11-2012
Abstract
We prove generalizations of Loewner's results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuting self-adjoint n-by-n matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone.
Recommended Citation
Agler, Jim; McCarthy, John E.; and Young, N J., "Operator monotone functions and Löwner functions of several variables" (2012). Mathematics Faculty Publications. 12.
https://openscholarship.wustl.edu/math_facpubs/12
Embargo Period
4-29-2013
Comments
This is the final author version of an article published in Annals of Mathematics 176 (2012), no. 3, 1783–1826. doi10.4007/annals.2012.176.3.7 Copyright © 2012 Annals of Mathematics Corrigendum published in 2014 see openscholarship.wustl.edu/facpubs/1