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Hilbert Spaces of Entire Functions and Composition Operators

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Abstract

The aim of this paper is to study composition operators on Hilbert spaces of entire functions in the complex plane \({\mathbb {C}}\). The following results are obtained: criteria for invariance and boundedness; estimates for essential norm, which give criteria for compactness of such operators; criteria for compact differences. Our results contain the results of boundedness and compactness by Chacón et al. (Proc Am Math Soc 135(7):2205–2218, 2007) as particular cases.

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Acknowledgments

The authors would like to thank the referees for useful remarks and comments that led to the improvement of this paper.

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Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), Singapore, 637371, Singapore

    Minh Luan Doan & Le Hai Khoi

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  1. Minh Luan Doan
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  2. Le Hai Khoi
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Correspondence to Le Hai Khoi.

Additional information

Communicated by Raymond Mortini.

Supported in part by MOE’s AcRF Tier 1 Grant M4011166.110 (RG24/13).

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Doan, M.L., Khoi, L.H. Hilbert Spaces of Entire Functions and Composition Operators. Complex Anal. Oper. Theory 10, 213–230 (2016). https://doi.org/10.1007/s11785-015-0497-0

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  • DOI: https://doi.org/10.1007/s11785-015-0497-0

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