非定域诱导（分数）束缚态：无限柯西势阱中的形状分析
Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well
摘要：
分数阶（Lévy型）算子被认为是空间非局部的。这成为一个问题，如果面对先验强加的外部狄利克雷边界数据。我们解决的柯西算子$(-Δ)^{1/2}$的原型例子在间隔$D=(-1,1) \subset R$的频谱特性，重点是最低本征函数的函数形状和他们的下降在边界的$D$。推导了新的高精度近似本征函数公式。我们分析了它们的形状再现保真度与相应特征值的评估精细度之间的关系。
英文摘要：
Fractional (Lévy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral properties of the prototype example of the Cauchy operator $(-Δ)^{1/2}$ in the interval $D=(-1,1) \subset R$, with a focus on functional shapes of lowest eigenfunctions and their fall-off at the boundaries of $D$. New high accuracy formulas are deduced for approximate eigenfunctions. We analyze how their shape reproduction fidelity is correlated with the evaluation finesse of the corresponding eigenvalues.
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