Journal article
A wedge-of-the-edge theorem: analytic continuation of multivariable Pick functions in and around the boundary
The Bulletin of the London Mathematical Society, v 49(5), pp 916-925
01 Oct 2017
Abstract
In 1956, quantum physicist N. Bogoliubov discovered the edge-of-the-wedge theorem, a theorem used to analytically continue a function through the boundary of a domain under certain conditions. We discuss an analogous phenomenon, a wedge-of-the-edge theorem, for the boundary values of Pick functions, functions from the poly upper half plane into the half plane. We show that Pick functions which have a continuous real-valued extension to a union of two hypercubes with a certain orientation in R-d have good analytic continuation properties. Furthermore, we establish bounds on the behavior of this analytic continuation, which makes normal families arguments accessible on the boundary for Pick functions in several variables. Moreover, we obtain a Hartog's phenomenon type result for locally inner functions.
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Details
- Title
- A wedge-of-the-edge theorem: analytic continuation of multivariable Pick functions in and around the boundary
- Creators
- J. E. Pascoe - Washington University in St. Louis
- Publication Details
- The Bulletin of the London Mathematical Society, v 49(5), pp 916-925
- Publisher
- Wiley
- Number of pages
- 10
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000412181900017
- Scopus ID
- 2-s2.0-85028439902
- Other Identifier
- 991021879626304721
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- Web of Science research areas
- Mathematics