Extension of Fréchet valued real analytic functions from subvarieties of ℝd

It is shown that for an algebraic subvariety X of ℝd every Fréchet valued real analytic function on X can be extended to a real analytic function on ℝd if and only if X is of type (PL), i.e. all of its singularities are of a certain type. Necessity of this condition is shown for any real analytic va...

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Bibliographic Details
Published in:Mathematische Nachrichten 2008-06, Vol.281 (6), p.903-911
Main Author: Vogt, Dietmar
Format: Article
Language:English
Subjects:
algebraic variety
Fréchet valued real analytic functions
Phragmén−Lindelöf condition
real analytic variety
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Summary:It is shown that for an algebraic subvariety X of ℝd every Fréchet valued real analytic function on X can be extended to a real analytic function on ℝd if and only if X is of type (PL), i.e. all of its singularities are of a certain type. Necessity of this condition is shown for any real analytic variety. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200710647