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Full-Text Articles in Analysis
Corrigendum To: Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, Nicholas J. Young
Corrigendum To: Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, Nicholas J. Young
All Faculty Publications
We fix a gap in the proof of Theorem 7.24 in Ann. of Math. 176 (2012), 1783–1826.
Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, N J. Young
Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, N J. Young
Mathematics Faculty Publications
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.
Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld
Combinatorial And Commutative Manipulations In Feynman's Operational Calculi For Noncommuting Operators, Duane Einfeld
Department of Mathematics: Dissertations, Theses, and Student Research
In Feynman's Operational Calculi, a function of indeterminates in a commutative space is mapped to an operator expression in a space of (generally) noncommuting operators; the image of the map is determined by a choice of measures associated with the operators, by which the operators are 'disentangled.' Results in this area of research include formulas for disentangling in particular cases of operators and measures. We consider two ways in which this process might be facilitated. First, we develop a set of notations and operations for handling the combinatorial arguments that tend to arise. Second, we develop an intermediate space for …
A Functional Calculus In A Non Commutative Setting, Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Daniele C. Struppa
A Functional Calculus In A Non Commutative Setting, Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity, see [6], and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.