Abstract
We define, for a compact subset K of complex Euclidean space containing the origin, the so-called Borel map (at the origin). We discuss its properties in detail and state, in the case when K is subanalytic, two conjectures relating the injectivity and surjectivity of the Borel map with properties of the polynomial hull of K. We give strong evidence for the validity of the conjectures (e.g. the open mapping property) and show that they are true when K is convex.
Original language | English |
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Article number | 172 |
Journal | Journal of Geometric Analysis |
Volume | 34 |
Issue number | 6 |
DOIs | |
Publication status | Published - Jun 2024 |
Austrian Fields of Science 2012
- 101002 Analysis
- 101009 Geometry
Keywords
- 32A38 (primary)
- 35N10
- Borel map
- Convex sets
- Fréchet algebras of functions
- Open mapping property
- Sub analytic sets