Eigenvalue estimates for the fractional Laplacian on lattice subgraphs
Abstract
We introduce the the fractional Laplacian on a subgraph of a graph with Dirichlet boundary condition. For a lattice graph, we prove the upper and lower estimates for the sum of the first k Dirichlet eigenvalues of the fractional Laplacian, extending the classical results by Li-Yau and Kr\"oger.
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