  Let $\Omega$ be an open set in $\R^d$ $(d > 1)$ and $h(\Omega)$ the Fr\'echet
space of harmonic functions on $\Omega$. Given a bounded linear operator
  $L :h(\Omega)\to h(\Omega)$, we show that its eigenvalues $\lambda_n$,
arranged in decreasing order and counting multiplicities, satisfy
  $|\lambda_n|\leq K\exp(-cn^{1/(d-1)})$, where $K$ and $c$ are two explicitly
computable positive constants.
