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Some Examples of Extremal Functions on the Dunkl-Type Fock Space \(F_k(\mathbb {C})\)

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Abstract

In this work, we recall some properties of the generalized Fock space \(F_k(\mathbb {C})\) and the Hilbert space \(H_k(\mathbb {C})\) (defined by the squared norm \(\Vert f\Vert ^2_{H_k(\mathbb {C})}:=\Vert f\Vert ^2_{F_k(\mathbb {C})}+\langle zf',f\rangle _{F_k(\mathbb {C})}\)). Next, we give the best approximation of the bounded operators \(L:F_k(\mathbb {C})\rightarrow H_k(\mathbb {C})\). As applications, we come up with some results regarding the approximate formulas for the difference operator, the Dunkl difference operator and the primitive operator.

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Acknowledgments

The author would like to express his deep thanks to the referee for her careful reading and her editing of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 277, Jazan, 45142, Saudi Arabia

    Fethi Soltani

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  1. Fethi Soltani
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Correspondence to Fethi Soltani.

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Communicated by Palle Jorgensen.

Author partially supported by the DGRST research project LR11ES11 and CMCU program 10G/1503.

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Soltani, F. Some Examples of Extremal Functions on the Dunkl-Type Fock Space \(F_k(\mathbb {C})\) . Complex Anal. Oper. Theory 10, 1501–1517 (2016). https://doi.org/10.1007/s11785-015-0484-5

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  • DOI: https://doi.org/10.1007/s11785-015-0484-5

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