Operator monotone functions and Löwner functions of several variables
Copyright policy )Operator monotone functions and Löwner functions of several variables
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.
- University of California, San Diego United States
- Washington University United States
- University of California, San Francisco United States
- Trinity College Dublin Ireland
- University of Mary United States
Functional calculus for linear operators, edge of the wedge, mathematics, Mathematics - Complex Variables, Several-variable operator theory (spectral, Fredholm, etc.), Loewner's theorem, functional calculus, operator monotone functions, Functional Analysis (math.FA), matrix monotone functions, Mathematics - Functional Analysis, 47A63, 32A35, edge of the wedge theorem, FOS: Mathematics, Norms of matrices, numerical range, applications of functional analysis to matrix theory, monotone operators, loewner class, Linear operator inequalities, loewner's theorem, Loewner class, Complex Variables (math.CV), Analysis
Functional calculus for linear operators, edge of the wedge, mathematics, Mathematics - Complex Variables, Several-variable operator theory (spectral, Fredholm, etc.), Loewner's theorem, functional calculus, operator monotone functions, Functional Analysis (math.FA), matrix monotone functions, Mathematics - Functional Analysis, 47A63, 32A35, edge of the wedge theorem, FOS: Mathematics, Norms of matrices, numerical range, applications of functional analysis to matrix theory, monotone operators, loewner class, Linear operator inequalities, loewner's theorem, Loewner class, Complex Variables (math.CV), Analysis
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).60 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!