English

Higher order Dirichlet-to-Neumann maps on graphs and their eigenvalues

Differential Geometry 2019-04-16 v3

Abstract

In this paper, we first introduce higher order Dirichlet-to-Neumann maps on graphs which can be viewed as a discrete analogue of the corresponding Dirichlet-to-Neumann maps on compact Riemannian manifolds with boundary and a higher order generalization of the Dirichlet-to-Neumann map on graphs introduced by Hua-Huang-Wang\cite{HHW} and Hassannezhad-Miclo \cite{HM}. Then, some Raulot-Savo-type estimates on the eigenvalues of the DtN maps introduced are derived.

Cite

@article{arxiv.1904.03880,
  title  = {Higher order Dirichlet-to-Neumann maps on graphs and their eigenvalues},
  author = {Yongjie Shi and Chengjie Yu},
  journal= {arXiv preprint arXiv:1904.03880},
  year   = {2019}
}

Comments

Some typos corrected and some details in computation added

R2 v1 2026-06-23T08:32:31.444Z