The Borel Map for Compact Subanalytic Subsets of Cm

Paulo D. Cordaro; Giuseppe Della Sala; Bernhard Lamel

doi:10.1007/s12220-024-01596-8

The Borel Map for Compact Subanalytic Subsets of Cm

Paulo D. Cordaro, Giuseppe Della Sala, Bernhard Lamel

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

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
Article number	172
Journal	Journal of Geometric Analysis
Volume	34
Issue number	6
DOIs	https://doi.org/10.1007/s12220-024-01596-8
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

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10.1007/s12220-024-01596-8

Cite this

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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.",

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AU - Cordaro, Paulo D.

AU - Sala, Giuseppe Della

AU - Lamel, Bernhard

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PY - 2024/6

Y1 - 2024/6

N2 - 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.

AB - 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.

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KW - Convex sets

KW - Fréchet algebras of functions

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KW - Sub analytic sets

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ER -

The Borel Map for Compact Subanalytic Subsets of Cm

Abstract

Austrian Fields of Science 2012

Keywords

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