Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

Volume 184 / 2008

José Bonet, Reinhold Meise Studia Mathematica 184 (2008), 49-77 MSC: Primary 42A85, 30D60; Secondary 46E10, 47B38. DOI: 10.4064/sm184-1-3

Abstract

Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space ${\mathcal E}_{(\omega)} (\mathbb R)$ of ($\omega$)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those ($\omega$)-ultradifferential operators which admit a continuous linear right inverse on ${\mathcal E}_{(\omega)} [a, b]$ for each compact interval $[a,b]$ and we show that this property is in fact weaker than the existence of a continuous linear right inverse on ${\mathcal E}_{(\omega)} (\mathbb R)$.

Authors

  • José BonetIMPA-UPV and Dpto. de Matemática Aplicada
    Universidad Politécnica de Valencia
    E-46071 Valencia, Spain
    e-mail
  • Reinhold MeiseMathematisches Institut
    Heinrich-Heine-Universität
    Universitätsstrasse 1
    40225 Düsseldorf, Germany
    e-mail

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