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

Yongjie Shi; Chengjie Yu

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arXiv · 1904.03880

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

Yongjie Shi·Chengjie Yu

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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.

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Yongjie Shi, Chengjie Yu. 2019-04-08. Higher order Dirichlet-to-Neumann maps on graphs and their eigenvalues. https://arxiv.org/abs/1904.03880

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