# Pluricapacity and approximation numbers of composition operators

Abstract : For suitable bounded hyperconvex sets $\Omega$ in $\C^N$, 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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Cited literature [19 references]

https://hal-univ-artois.archives-ouvertes.fr/hal-01877752
Contributor : Daniel Li <>
Submitted on : Thursday, September 20, 2018 - 12:03:46 PM
Last modification on : Sunday, November 29, 2020 - 3:24:16 AM
Long-term archiving on: : Friday, December 21, 2018 - 2:15:41 PM

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### Identifiers

• HAL Id : hal-01877752, version 1
• ARXIV : 1809.08864

### Citation

Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. Pluricapacity and approximation numbers of composition operators. 2018. ⟨hal-01877752⟩

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