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Analytic Extension of Non Quasi ‐ Analytic Whitney Jets of Beurling Type
Author(s) -
Schmets Jean,
Valdivia Manuel
Publication year - 1998
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.19981950111
Subject(s) - mathematics , analytic function , type (biology) , extension (predicate logic) , class (philosophy) , combinatorics , function (biology) , regular polygon , sequence (biology) , mathematical analysis , pure mathematics , geometry , ecology , genetics , artificial intelligence , evolutionary biology , computer science , biology , programming language
Let ( M r ) r ∈ ℕ0 be a logarithmically convex sequence of positive numbers which verifies M 0 = 1 as well as M r ≥ 1 for every r ∈ ℕ and defines a non quasi ‐ analytic class. Let moreover F be a closed proper subset of ℝ n . Then for every function f on ℝ n belonging to the non quasi ‐ analytic ( M r )‐class of Beurling type, there is an element g of the same class which is analytic on ℝ, n F and such that D α f ( x ) = D α g ( x ) for every α ∈ ℕ n 0 and x ∈ F .