Eigenvalue distribution of invariant linear second order elliptic differential operators with constant coefficients (Q687223)

Summary: Let \({\mathfrak G}\) be a properly discontinuous group of affine transformations acting on an \(n\)-dimensional affine space and \(P\) a \({\mathfrak G}\)-invariant linear elliptic differential operator with constant coefficients. In this paper the \({\mathfrak G}\)-automorphic eigenvalue problem to \(P\) is solved. For the number \(N(\lambda)\) of the eigenvalues which are less than or equal to the ``frequency bound'' \(\lambda^ 2\) the asymptotic estimation \(N(\lambda) = c_ 0 \lambda^ n + c_ 1 \lambda^{n-1} + O (\lambda^{n - 2 + 2/(n + 1)})\) is given with \(c_ 0\) and \(c_ 1\) being interesting geometric invariants.