Abstract
Let Ω be an open set in ℝd (d > 1) and let h(Ω) be the Fréchet space of harmonic functions on Ω. Given a bounded linear operator L : h (Ω) → h(Ω), we show that its eigenvalues λn, arranged in decreasing order and counting multiplicities, satisfy |λn| ⩽ K exp(−cn1/(d−1)), where K and c are two explicitly computable positive constants.
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