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Admissible functions for the Dirichlet space

Volume 198 / 2010

Javad Mashreghi, Mahmood Shabankhah Studia Mathematica 198 (2010), 147-156 MSC: Primary 30C15; Secondary 30J10, 30H10, 31C25. DOI: 10.4064/sm198-2-3

Abstract

Zero sets and uniqueness sets of the classical Dirichlet space $\mathcal{D}$ are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for $\mathcal{D}$. Then we discuss the relation between the zero sets of $\mathcal{D}$ and those of $\mathcal{A}^\infty$.

Authors

  • Javad MashreghiDépartement de mathématiques et de statistique
    Université Laval
    Québec, QC, Canada G1K 7P4
    e-mail
  • Mahmood ShabankhahCMI, LATP
    Université de Provence
    39, Rue F. Joliot-Curie
    13453 Marseille Cedex 13, France
    e-mail

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