Geodesic
Operator monotone functions and Löwner functions of several variables
Jim Agler1 ; John E. McCarthy2 ; N. J. Young3
1 Department of Mathematics, UC San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093-0112
2 Mathematics Department, Washington University in St. Louis, St. Louis, MO 63130 and<br/> School of Mathematics, Trinity College, Dublin 2, Ireland
3 School o Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom, and<br/> School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne NE3 4LR, United Kingdom
Annals of mathematics, Tome 176 (2012) no. 3, pp. 1783-1826.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2012.176.3.7

Jim Agler 1 ; John E. McCarthy 2 ; N. J. Young 3

1 Department of Mathematics, UC San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093-0112
2 Mathematics Department, Washington University in St. Louis, St. Louis, MO 63130 and<br/> School of Mathematics, Trinity College, Dublin 2, Ireland
3 School o Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom, and<br/> School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne NE3 4LR, United Kingdom 
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Jim Agler; John E. McCarthy; N. J. Young. Operator monotone functions and Löwner functions of several variables. Annals of mathematics, Tome 176 (2012) no. 3, pp. 1783-1826. doi : 10.4007/annals.2012.176.3.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.3.7/

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