Journal article
AUTOMATIC REAL ANALYTICITY AND A REGAL PROOF OF A COMMUTATIVE MULTIVARIATE LOWNER THEOREM
Proceedings of the American Mathematical Society, v 149(5), pp 2019-2024
01 May 2021
Abstract
We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of functions must be real analytic if they have certain nice properties on one-dimensional slices. Let E subset of R-d be open. A function f : E -> R is matrix monotone lite if f (phi(1)(t), ..., phi(d)(t)) is a matrix monotone function of t whenever t is an element of (0, 1), the phi(i) are automorphisms of the upper half plane, and the tuple (phi(1)(t), ..., phi(d)(t)) maps (0, 1) into E. We use the "royal road" to show that a function is matrix monotone lite if and only if it analytically continues to the multivariate upper half plane as a map into the upper half plane. Moreover, matrix monotone lite functions in two variables are locally matrix monotone in the sense of Agler-McCarthy-Young.
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Details
- Title
- AUTOMATIC REAL ANALYTICITY AND A REGAL PROOF OF A COMMUTATIVE MULTIVARIATE LOWNER THEOREM
- Creators
- J. E. Pascoe - University of FloridaRyan Tully-Doyle - University of New Haven
- Publication Details
- Proceedings of the American Mathematical Society, v 149(5), pp 2019-2024
- Publisher
- Amer Mathematical Soc
- Number of pages
- 6
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000631285900017
- Scopus ID
- 2-s2.0-85103031682
- Other Identifier
- 991021879630604721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied