The Borel map for compact sets in the plane
- Author(s)
- Paulo D. Cordaro, Giuseppe Della Sala, Bernhard Lamel
- Abstract
We discuss the Borel map at a point p∈Kˆ, where Kˆ is the polynomially convex hull of the compact set K⊂C, associating to every function f∈A∞(K) its formal Taylor series at p, and show that it satisfies an alternative (provided that K fulfills a mild condition): It is either surjective or injective, and the latter is the case if and only if p∈Kˆ∘. We also discuss variants of this result for approximation by rational functions and a smooth version of the Mergelyan theorem.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- University of São Paulo, American University of Beirut
- Journal
- Journal of Functional Analysis
- Volume
- 278
- Pages
- 108402
- No. of pages
- 17
- ISSN
- 0022-1236
- DOI
- https://doi.org/10.1016/j.jfa.2019.108402
- Publication date
- 04-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis
- Keywords
- ASJC Scopus subject areas
- Analysis
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/the-borel-map-for-compact-sets-in-the-plane(98d308c3-b6dd-4eba-8397-eeb72cef31d2).html