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The Discrete Laplacian Acting on 2-Forms and Application

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Abstract

In the current paper, we study the discrete Laplacian acting on 2-forms which was introduced and investigated by Chebbi (Potential Anal 49(2):331–358, 2018). We establish a new criterion of essential self-adjointness using the Nelson lemma. Moreover, we give an upper bound on the infimum of the essential spectrum. Furthermore, we establish a link between the adjacency matrix and the discrete Laplacian on 2-forms.

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Acknowledgements

The authors thank Colette Anné, Nabila Torki-Hamza, Sylvain Golénia and Nassim Athmouni for useful discussions and comments on the text. They would like to thank also the anonymous referee for their numerous relevant remarks and useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Gafsa, University of Gafsa, 2112, Zarroug, Gafsa, Tunisia

    Hatem Baloudi

  2. Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, 3000, Sfax, Tunisia

    Sayda Belgacem & Aref Jeribi

Authors
  1. Hatem Baloudi
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  2. Sayda Belgacem
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  3. Aref Jeribi
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Correspondence to Hatem Baloudi.

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Communicated by Mohammad Sal Moslehian.

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Baloudi, H., Belgacem, S. & Jeribi, A. The Discrete Laplacian Acting on 2-Forms and Application. Bull. Malays. Math. Sci. Soc. 43, 1025–1045 (2020). https://doi.org/10.1007/s40840-019-00721-z

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  • DOI: https://doi.org/10.1007/s40840-019-00721-z

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