The Bergmann-Shilov boundary of a bounded symmetric domain
Michael Mackey, Pauline Mellon
TL;DR
This paper investigates the boundary sets of bounded symmetric domains that uniquely determine holomorphic functions and extends the concept of the Bergmann-Shilov boundary to finite rank JB*-triples.
Contribution
It introduces an analogue of the Bergmann-Shilov boundary for finite rank JB*-triples, expanding boundary theory in complex analysis.
Findings
Identifies boundary sets that determine holomorphic functions and their norms.
Extends classical boundary concepts to JB*-triples.
Provides new tools for boundary analysis in complex domains.
Abstract
We show that there are many sets in the boundary of a bounded symmetric domain that determine the values and norm of holomorphic functions on the domain having continuous extensions to the boundary. We provide an analogue of the Bergmann-Shilov boundary for finite rank JB*-triples.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Meromorphic and Entire Functions