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We study the eigenvalues of the Dirichlet-to-Neumann operator on a finitesubgraph of the integer lattice Zn. We estimate the first n+1 eigenvalues usingthe number of vertices of the subgraph. As a corollary, we prove that the firstnon-trivial eigenvalue of the Dirichlet-to-Neumann operator tends to zero asthe number of vertices of the subgraph tends to infinity.

Steklov Eigenvalue Problem on Subgraphs of Integer Lattices