Operator monotone functions and Löwner functions of several variables
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- Professor Jim Agler
- Professor Nicholas Young
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| Author(s) | | Agler J, McCathy JE, Young NJ |
| Publication type | | Article |
| Journal | | Annals of Mathematics |
| Year | | 2012 |
| Volume | | 176 |
| Issue | | 3 |
| Pages | | 1783-1826 |
| ISSN (print) | | 0003-486X |
| ISSN (electronic) | | 1939-8980 |
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| Full text is available for this publication: |
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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. |
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| 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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