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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