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 $$q\ge 2$$ is a fixed integer. We also give an estimate on the approximation numbers of such an operator.