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.
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Acknowledgements
The authors thank the referee for many useful comments. The first author thanks the Council of Scientific and Industrial Research (CSIR), India, for providing financial support in the form of a SPM Fellowship to carry out this research. The third author thanks the Indian Statistical Institute of Chennai for providing good and friendly working conditions in December 2015, when this collaboration was initiated. The second author is currently at ISI Chennai.
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Muthukumar, P., Ponnusamy, S. & Queffélec, H. Estimate for Norm of a Composition Operator on the Hardy–Dirichlet Space. Integr. Equ. Oper. Theory 90, 11 (2018). https://doi.org/10.1007/s00020-018-2434-x
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DOI: https://doi.org/10.1007/s00020-018-2434-x