Rational approximation on products of planar domains [article]

Richard M. Aron, Paul M. Gauthier, Manuel Maestre, Vassili Nestoridis, Javier Falcó, University, My, University, My
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.
doi:10.34657/3074 fatcat:zjqot4fvkbby7nrthtovaijibm