New Explicitly Diagonalizable Hankel Matrices Related to the Stieltjes–Carlitz Polynomials

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 ℓ 2 ( 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.