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Gross Laplacian Acting on Operators

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Abstract

In this paper, we introduce a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian, acting on some analytical operators. For this purpose, we use a characterization theorem between this class of operators and their symbols. Applying the quantum Gross Laplacian to the particular case where the operator is the multiplication one, we establishes a relation between the classical and the quantum Gross Laplacians.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 1060, Tunis, Tunisia

    Samah Horrigue & Habib Ouerdiane

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  1. Samah Horrigue
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  2. Habib Ouerdiane
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Correspondence to Habib Ouerdiane.

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Horrigue, S., Ouerdiane, H. Gross Laplacian Acting on Operators. Acta Appl Math 105, 227–239 (2009). https://doi.org/10.1007/s10440-008-9273-8

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  • DOI: https://doi.org/10.1007/s10440-008-9273-8

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