Author's School

Arts & Sciences

Author's Department

Mathematics

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.

Comments

This is the final author version of an article published in Annals of Mathematics 176 (2012), no. 3, 1783–1826. doi:10.4007/annals.2012.176.3.7

Copyright © 2012 Annals of Mathematics

Corrigendum published in 2014 see openscholarship.wustl.edu/facpubs/1

Embargo Period

4-29-2013

Included in

Analysis Commons

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