Browsing by Author "Nestoridis, Vassili"

Now showing 1 - 5 of 5
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    A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2019) Falcó, Javier; Gauthier, Paul Montpetit; Manolaki, Myrto; Nestoridis, Vassili
    For compact sets K⊂Cd, we introduce a subalgebra AD(K) of A(K), which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
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    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.
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    Non-extendability of holomorphic functions with bounded or continuously extendable derivatives
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Moschonas, Dionysios; Nestoridis, Vassili
    We consider the spaces H∞F(Ω) and AF(Ω) containing all holomorphic functions f on an open set Ω⊆C, such that all derivatives f(l), l∈F⊆N0={0,1,...}, are bounded on Ω, or continuously extendable on Ω¯¯¯¯, respectively. We endow these spaces with their natural topologies and they become Fr\'echet spaces. We prove that the set S of non-extendable functions in each of these spaces is either void, or dense and Gδ. We give examples where S=∅ or not. Furthermore, we examine cases where F can be replaced by F˜={l∈N0:minF⩽l⩽supF}, or F˜0={l∈N0:0⩽l⩽supF} and the corresponding spaces stay unchanged.
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    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.
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    Spherical arc-length as a global conformal parameter for analytic curves in the Riemann sphere
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Gauthier, Paul; Nestoridis, Vassili; Papadopoulos, Athanase
    We prove that for every analytic curve in the complex plane C, Euclidean and spherical arc-lengths are global conformal parameters. We also prove that for any analytic curve in the hyperbolic plane, hyperbolic arc-length is also a global parameter. We generalize some of these results to the case of analytic curves in Rn and Cn and we discuss the situation of curves in the Riemann sphere C {∞}.