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Gross Laplacian Acting on Operators |
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| Authors: | Samah Horrigue Habib Ouerdiane |
| Institution: | (1) Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar, 1060 Tunis, Tunisia |
| 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. |
| Keywords: | Space of entire functions with growth condition Symbols and kernels of operators Convolution product Classical and quantum Gross Laplacian |
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