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Extension of Fréchet valued real analytic functions from subvarieties of ℝ d
Author(s) -
Vogt Dietmar
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710647
Subject(s) - subvariety , mathematics , analytic function , extension (predicate logic) , type (biology) , gravitational singularity , variety (cybernetics) , function (biology) , pure mathematics , algebraic number , algebraic variety , mathematical analysis , statistics , ecology , evolutionary biology , computer science , biology , programming language
It is shown that for an algebraic subvariety X of ℝ d every Fréchet valued real analytic function on X can be extended to a real analytic function on ℝ d 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)
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