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New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials
Integral Equations and Operator Theory ( IF 0.8 ) Pub Date : 2021-05-26 , DOI: 10.1007/s00020-021-02638-4
František Štampach , Pavel Šťovíček

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:

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。

更新日期:2021-05-26
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