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Journal article
Analytic Continuation of Concrete Realizations and the McCarthy Champagne Conjecture
International mathematics research notices, v 2023(9), pp 7845-7882
04 May 2023
Abstract
In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz, and Pick functions, without adding additional singularities except perhaps poles coming from the conformal transformation itself. In the two-variable commutative case, we use a canonical de Branges-Rovnyak model theory to obtain concrete realizations that analytically continue through the boundary for inner functions that are rational in one of the variables (so-called quasirational functions). We then establish a positive solution to McCarthy's Champagne conjecture for local to global matrix monotonicity in the settings of both two-variable quasi-rational functions and d-variable perspective functions.
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Details
- Title
- Analytic Continuation of Concrete Realizations and the McCarthy Champagne Conjecture
- Creators
- Kelly Bickel - Bucknell UniversityJ. E. Pascoe - University of FloridaRyan Tully-Doyle - Cal Poly SLO, Dept Math, 1 Grand Ave, San Luis Obispo, CA 93410 USA
- Publication Details
- International mathematics research notices, v 2023(9), pp 7845-7882
- Publisher
- Oxford Univ Press
- Number of pages
- 38
- Grant note
- 1606260 / NSF-DMS Mathematical Science Postdoctoral Research Fellowship 1953963 / Division Of Mathematical Sciences; Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) 1953963 / NSF-DMS Analysis 1606260; 2000088 / Direct For Mathematical & Physical Scien; Division Of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) 2000088 / NSF-DMS Analysis grant
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000802306100001
- Scopus ID
- 2-s2.0-85160960409
- Other Identifier
- 991021879788204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics