English

The discrete Laplacian of a 2-simplicial complex

Spectral Theory 2018-02-26 v1 Functional Analysis

Abstract

In this paper, we introduce the notion of oriented faces especially triangles in a connected oriented locally finite graph. This framework then permits to define the Laplace operator on this structure of the 2-simplicial complex. We develop the notion of χ\chi-completeness for the graphs, based on the cutoff functions. Moreover, we study essential self-adjointness of the discrete Laplacian from the χ\chi-completeness geometric hypothesis.

Keywords

Cite

@article{arxiv.1802.08422,
  title  = {The discrete Laplacian of a 2-simplicial complex},
  author = {Yassin Chebbi},
  journal= {arXiv preprint arXiv:1802.08422},
  year   = {2018}
}