Journal article
Cauchy transforms arising from homomorphic conditional expectations parametrize noncommutative Pick functions
Journal of mathematical analysis and applications, v 472(2), pp 1487-1498
15 Apr 2019
Abstract
Nevanlinna showed that Cauchy transforms of probability measures parametrize all functions from the upper half plane into itself satisfying a certain asymptotic condition at infinity. We show that the correspondence fails in general for the unbounded case for somewhat trivial reasons; however, we show that in a setting of “homomorphic” operator valued free probability that Cauchy transforms of homomorphic conditional expectations parametrize noncommutative Pick functions.
Metrics
Details
- Title
- Cauchy transforms arising from homomorphic conditional expectations parametrize noncommutative Pick functions
- Creators
- J.E. Pascoe - Washington University in St. LouisRyan Tully-Doyle - University of New Haven
- Publication Details
- Journal of mathematical analysis and applications, v 472(2), pp 1487-1498
- Publisher
- Elsevier
- Grant note
- DMS 1606260 / National Science Foundation (https://doi.org/10.13039/100000001)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000456359000012
- Scopus ID
- 2-s2.0-85058231854
- Other Identifier
- 991021879626804721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied