满足Sierpinski三角形的特征值问题：计算非自伴随机算子的谱
Eigenvalue problem meets Sierpinski triangle: computing the spectrum of a non-self-adjoint random operator
摘要：
本文证明了Feinberg和A. Zee（Phys.Rev.E59（1999），6433- 6443）具有内点。我们这样做，首先回顾，这个随机算子的频谱是一组$\ell^\infty$特征值的所有无限矩阵具有相同的结构。然后，我们构建了一个无限矩阵的这种结构的每一个点的开放单位盘是一个$\ell^\infty$特征值，这是从以下事实，即特征向量的组件是多项式的频谱参数，其非零系数是$\pm 1$的，形成一个无限的离散Sierpinski三角形的模式。
英文摘要：
The purpose of this paper is to prove that the spectrum of the non-self-adjoint one-particle Hamiltonian proposed by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433--6443) has interior points. We do this by first recalling that the spectrum of this random operator is the union of the set of $\ell^\infty$ eigenvalues of all infinite matrices with the same structure. We then construct an infinite matrix of this structure for which every point of the open unit disk is an $\ell^\infty$ eigenvalue, this following from the fact that the components of the eigenvector are polynomials in the spectral parameter whose non-zero coefficients are $\pm 1$'s, forming the pattern of an infinite discrete Sierpinski triangle.
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