Composition operators on spaces of double Dirichlet series (Q2228345)

The authors study composition operators \(C_\phi: f\mapsto f\circ\phi\) on \(\mathcal H^\infty(\mathbb C^2_+)\), the space of those bounded holomorphic functions \(f(s)\) on the Cartesian product of the right half-plane \(\mathbb C_+\) with itself and which admit a representation as a double Dirichlet series \(\sum_{m,n} a_{m,n}m^{s}n^{-s}\). The one-variable case is also revisited. In this latter setting, the authors also consider superposition operators \(S_\varphi:f\mapsto \varphi \circ f\) on certain subspaces of the set of Dirichlet series.