Operator monotone functions and Löwner functions of several variables
 Lookup NU author(s)
 Professor Jim Agler
 Professor Nicholas Young
 John Cunningham




Author(s)   Agler J, McCathy JE, Young NJ 
Publication type   Article 
Journal   Annals of Mathematics 
Year   2012 
Volume   176 
Issue   3 
Pages   17831826 
ISSN (print)   0003486X 
ISSN (electronic)   19398980 



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We prove generalizations of Löwner’s results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on dtuples of commuting selfadjoint nbyn matrices. We prove a generalization to several variables of Nevanlinna’s theorem describing analytic functions that map the upper halfplane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone. 



Publisher   Mathematical Sciences Publishers 
URL   http://dx.doi.org/10.4007/annals.2012.176.3.7 
DOI   10.4007/annals.2012.176.3.7 

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