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arXiv · 1809.08864

Pluricapacity and approximation numbers of composition operators

Daniel Li·Hervé Queffélec·Luis Rodríguez-Piazza·Hervé Queélec
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Abstract

For suitable bounded hyperconvex sets $\Omega$ in $\mathbb{C}^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_\phi \colon H^2 (\Omega) \to H^2 (\Omega)$ when $\phi (\Omega)$ is relatively compact in $\Omega$, involving the Monge-Amp\`ere capacity of $\phi (\Omega)$.

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Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza, Hervé Queélec. 2018-09-24. Pluricapacity and approximation numbers of composition operators. https://arxiv.org/abs/1809.08864

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