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On the Range of Two Convolution Operators
Author(s) -
Fernández Carmen
Publication year - 2000
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 - 10.1002/1522-2616(200008)216:1<61::aid-mana61>3.0.co;2-a
Subject(s) - mathematics , convolution (computer science) , class (philosophy) , range (aeronautics) , type (biology) , pure mathematics , work (physics) , inclusion (mineral) , algebra over a field , artificial intelligence , computer science , social psychology , psychology , ecology , materials science , artificial neural network , composite material , biology , mechanical engineering , engineering
Let $\cal E$ ( ω ) (ℝ) denote the non–quasianalytic class of Beurling type on ℝ. For μ , ν ∈ $\cal E$ ′ ( ω ) (ℝ) we give necessary conditions for the inclusion T ν ( $\cal E$ ( ω ) (ℝ)) ⊂ T μ ( $\cal E$ ( ω ) (ℝ)), thus extending previous work of Malgrange and Ehrenpreis .