Operator monotone functions and Lowner functions of several variables

• 成果类型: Article
• 署名作者: Agler, Jim; McCarthy, John E.; Young, N. J.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.3.7
• 发表日期: 2012
• 页码: 1783-1826
• 关键词: nevanlinna-pick interpolation; BOUNDARY; THEOREM

摘要

We prove generalizations of Lowner'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.