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 $\phi (s)=c_1+c_q{q}^{-s}$ where $q\ge 2$ is a fixed integer. We also give an estimate on the approximation numbers of such an operator.

12 pages, one figure; To appear in Integral Equations and Operator Theory