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The discrete Laplacian acting on 2-forms and application. (English) Zbl 1434.05087

Summary: In the current paper, we study the discrete Laplacian acting on 2-forms which was introduced and investigated by Y. Chebbi [Potential Anal. 49, No. 2, 331–358 (2018; Zbl 1395.05095)]. 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.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)

Citations:

Zbl 1395.05095
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References:

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