Estimate for norm of a composition operator on the Hardy-Dirichlet space

Abstract

By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on $\mathcal{H}^2$, the space of Dirichlet series with square summable coefficients, for the inducing symbol $\varphi(s)=c_1+c_{q}q^{-s}$ where $q\geq 2$ is a fixed integer. We also give an estimate on the approximation numbers of such an operator.