On finite subgraphs of the integer lattice, the average of the first k Dirichlet poly-Laplace eigenvalues obeys explicit upper and lower bounds of Weyl form, and 2l-order eigenvalues dominate squares of l-order eigenvalues.
On kernels, eigenvalues, and eigenfuncti ons of operators related to elliptic problems
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Eigenvalue estimates for the poly-Laplace operator on lattice subgraphs
On finite subgraphs of the integer lattice, the average of the first k Dirichlet poly-Laplace eigenvalues obeys explicit upper and lower bounds of Weyl form, and 2l-order eigenvalues dominate squares of l-order eigenvalues.