New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials
Abstract
Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter k∈(0,1) are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space 2(N0) 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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