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arXiv · 1911.07059

On Hankel matrices commuting with Jacobi matrices from the Askey scheme

František Štampach·Pavel Šťovíček
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Abstract

A complete characterization is provided of Hankel matrices commuting with Jacobi matrices which correspond to hypergeometric orthogonal polynomials from the Askey scheme. It follows, as the main result of the paper, that the generalized Hilbert matrix is the only prominent infinite-rank Hankel matrix which, if regarded as an operator on $\ell^{2}(\mathbb{N}_{0})$, is diagonalizable by application of the commutator method with Jacobi matrices from the mentioned families.

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František Štampach, Pavel Šťovíček. 2019-11-16. On Hankel matrices commuting with Jacobi matrices from the Askey scheme. https://arxiv.org/abs/1911.07059

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