Journal article
Free Pick functions: Representations, asymptotic behavior and matrix monotonicity in several noncommuting variables
Journal of functional analysis, v 273(1), pp 283-328
01 Jul 2017
Abstract
R. Nevanlinna showed that elements of the Pick class, the set of complex analytic functions taking the upper half plane into itself, have certain integral representations which reflect their asymptotic behavior at infinity. Later, Löwner connected the Pick class to matrix monotone functions. We generalize the Nevanlinna representation theorems and Löwner's theorem on matrix monotone functions to the free Pick class, the collection of functions that map tuples of matrices with positive imaginary part into the matrices with positive imaginary part which obey the free functional calculus.
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Details
- Title
- Free Pick functions: Representations, asymptotic behavior and matrix monotonicity in several noncommuting variables
- Creators
- J.E. Pascoe - Washington University in St. LouisR. Tully-Doyle - Hampton University
- Publication Details
- Journal of functional analysis, v 273(1), pp 283-328
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000401785200005
- Scopus ID
- 2-s2.0-85017391626
- Other Identifier
- 991021879784204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics