Operator monotone functions and Löwner functions of several variables

  1. Lookup NU author(s)
  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
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
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