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

Institut für Mathematik

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › 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.

Originalsprache	Englisch
Aufsatznummer	172
Fachzeitschrift	Journal of Geometric Analysis
Jahrgang	34
Ausgabenummer	6
DOIs	https://doi.org/10.1007/s12220-024-01596-8
Publikationsstatus	Veröffentlicht - Juni 2024

Fördermittel

G. Della Sala was supported by the Center for Advanced Mathematical Sciences (CAMS), http://orcid.org/0009-0004-5763-5004 by a grant from the University Research Board of AUB, and also by CNPq (Brazil). Paulo D. Cordaro was partially supported by grants from CNPq and FAPESP (2018/14316-3), both from Brazil. Bernhard Lamel was supported by the Austrian Science Fund FWF, Project I4557. Bernhard Lamel is partially supported by the Qatar National Research Fund, project NPRP BSRA01-0309-210004, and by the Austrian Science Fund FWF, project AI4557.

ÖFOS 2012

101002 Analysis
101009 Geometrie

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KW - Fréchet algebras of functions

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The Borel Map for Compact Subanalytic Subsets of Cm

Abstract

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ÖFOS 2012

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