English

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

Spectral Theory 2019-11-20 v1 Classical Analysis and ODEs

Abstract

Four new examples of explicitly diagonalizable Hankel matrices depending on a parameter k(0,1)k\in(0,1) are presented. The Hankel matrices are regarded as matrix operators on the Hilbert space 2(N0)\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.

Keywords

Cite

@article{arxiv.1911.08218,
  title  = {New explicitly diagonalizable Hankel matrices related to the Stieltjes-Carlitz polynomials},
  author = {František Štampach and Pavel Šťovíček},
  journal= {arXiv preprint arXiv:1911.08218},
  year   = {2019}
}