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arXiv · 1911.08218

New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials

František Štampach·Pavel Šťovíček
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Abstract

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.

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František Štampach, Pavel Šťovíček. 2019-11-19. New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials. https://arxiv.org/abs/1911.08218

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