Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter \(k\in (0,1)\) are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space \(\ell ^{2}(\mathbb {N}_{0})\) and the solution of the spectral problem is based on an application of the commutator method. Each of the Hankel matrices commutes with a Jacobi matrix which is related to a particular family of the Stieltjes–Carlitz polynomials. More examples of explicitly diagonalizable structured matrix operators are obtained when taking into account also weighted Hankel matrices.

中文翻译：

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与Stieltjes-Carlitz多项式有关的新的显式对角化Hankel矩阵

给出了根据参数\（k \ in（0,1）\）显式对角化Hankel矩阵的四个新示例。Hankel矩阵被视为希尔伯特空间\（\ ell ^ {2}（\ mathbb {N} _ {0}）\）上的矩阵算子，并且频谱问题的解决方案基于换向器方法的应用。每个Hankel矩阵都与Jacobi矩阵交换，该Jacobi矩阵与Stieltjes-Carlitz多项式的特定族有关。当还考虑加权的汉克尔矩阵时，可以获得可显式对角化的结构化矩阵算子的更多示例。