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Journal article
Representation of Free Herglotz Functions
Indiana University mathematics journal, v 68(4), pp 1199-1215
01 Jan 2019
Abstract
A Herglotz function is a holomorphic map from the open complex unit disk into the closed complex right half plane. A classical Herglotz function has an integral representation against a positive measure on the unit circle. We prove a free analytic analogue of the Herglotz representation and describe how our representations specialize to the free probabilistic case. We also show that the set of representable Herglotz functions arising from noncommutative conditional expectations must be closed in a natural topology.
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Details
- Title
- Representation of Free Herglotz Functions
- Creators
- J. E. Pascoe - Washington Univ, Dept Math, One Brookings Dr, St Louis, MO 63130 USABenjamin Passer - University of WaterlooRyan Tully-Doyle - University of New Haven
- Publication Details
- Indiana University mathematics journal, v 68(4), pp 1199-1215
- Publisher
- Indiana Univ Math Journal
- Number of pages
- 17
- Grant note
- Zuckerman fellowship at the Technion DMS 1606260 / National Science Foundation Mathematical Science Postdoctoral Research Fellowship; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000484366600006
- Scopus ID
- 2-s2.0-85072932121
- Other Identifier
- 991021879628604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics