Eigenvalue decay of operators on harmonic function spaces

Details Eigenvalue decay of operators on harmonic function spaces Eigenvalue decay of operators on harmonic function spaces

2009-03-05

arxiv.org/abs/0903.0865v1

Mathematics

Functional Analysis

AMS-LaTeX, 14 pages

Scientific paper

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.

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