Operator monotone functions and Löwner functions of several variables

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  2. Professor Jim Agler
  3. Professor Nicholas Young
  4. John Cunningham
Author(s)Agler J, McCathy JE, Young NJ
Publication type Article
JournalAnnals of Mathematics
Year2012
Volume176
Issue3
Pages1783-1826
ISSN (print)0003-486X
ISSN (electronic)1939-8980
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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 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.
PublisherMathematical Sciences Publishers
URLhttp://dx.doi.org/10.4007/annals.2012.176.3.7
DOI10.4007/annals.2012.176.3.7
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