Browsing by Author "Maestre, Manuel"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Analytic structure in fibers
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Aron, Richard M.; Falcó, Javier; García, Domingo; Maestre, Manuel
    Let BX be the open unit ball of a complex Banach space X, and let H∞(BX) and Au(BX) be, respectively, the algebra of bounded holomorphic functions on BX and the subalgebra of uniformly continuous holomorphic functions on BX. In this paper we study the analytic structure of fibers in the spectrum of these two algebras. For the case of H∞(BX), we prove that the fiber in M(H∞(Bc0)) over any point of the distinguished boundary of the closed unit ball B¯ℓ∞ of ℓ∞ contains an analytic copy of Bℓ∞. In the case of Au(BX) we prove that if there exists a polynomial whose restriction to the open unit ball of X is not weakly continuous at some point, then the fiber over every point of the open unit ball of the bidual contains an analytic copy of D.
  • Thumbnail Image
    Item
    Dirichlet approximation and universal dirichlet series
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Aron, Richard M.; Bayart, Frédéric; Gauthier, Paul M.; Maestre, Manuel; Nestoridis, Vassili
    We characterize the uniform limits of Dirichlet polynomials on a right half plane. We extend the approximation theorems of Runge,Mergelyan and Vitushkin to the Dirichlet setting with respect to the Euclidean distance and to the chordal one, as well. We also strengthen the notion of Universal Dirichlet series.
  • Thumbnail Image
    Item
    Dirichlet Series and Function Theory in Polydiscs
    (Zürich : EMS Publ. House, 2014) Maestre, Manuel; Saksman, Eero; Seip, Kristian
    The interaction between Dirichlet series and function theory in polydiscs dates back to a fundamental insight of Harald Bohr and the subsequent groundbreaking work on multilinear forms and polarization by Bohnenblust and Hille. Since around 1997, there has been a revival of interest in the research area opened up by these early contributions. The workshop reflected the status of the field and led to fruitful discussions on problems of current interest and future research directions.
  • Thumbnail Image
    Item
    Rational approximation on products of planar domains
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Aron, Richard M.; Gauthier, Paul M.; Maestre, Manuel; Nestoridis, Vassili; Falcó, Javier
    We consider A(Ω), the Banach space of functions f from Ω¯¯¯¯=∏i∈IUi¯¯¯¯¯ to C that are continuous with respect to the product topology and separately holomorphic, where I is an arbitrary set and Ui are planar domains of some type. We show that finite sums of finite products of rational functions of one variable with prescribed poles off Ui¯¯¯¯¯ are uniformly dense in A(Ω). This generalizes previous results where Ui=D is the open unit disc in C or Ui¯¯¯¯¯c is connected.