调和函数空间上算子的Eigenvalue衰变
Eigenvalue decay of operators on harmonic function spaces
摘要：
设$Ω$是$\R^d$ $(d > 1)$中的开集，$h(Ω)$是$Ω$上调和函数的Fréchet空间.给定一个有界线性算子$L :h(Ω)\to h(Ω)$，我们证明了其特征值$λ_n$，按降序排列并计数重数，满足$|λ_n|\leq K\exp(-cn^{1/(d-1)})$，其中$K$和$c$是两个显式可计算的正常数.
英文摘要：
Let $Ω$ be an open set in $\R^d$ $(d > 1)$ and $h(Ω)$ the Fréchet space of harmonic functions on $Ω$. Given a bounded linear operator $L :h(Ω)\to h(Ω)$, we show that its eigenvalues $λ_n$, arranged in decreasing order and counting multiplicities, satisfy $|λ_n|\leq K\exp(-cn^{1/(d-1)})$, where $K$ and $c$ are two explicitly computable positive constants.
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