Self-adjoint difference operators and classical solutions to the Stieltjes-Wigert moment problem

@article{Christiansen2006SelfadjointDO,
  title={Self-adjoint difference operators and classical solutions to the Stieltjes-Wigert moment problem},
  author={Jacob S. Christiansen and Erik Koelink},
  journal={Journal of Approximation Theory},
  year={2006},
  volume={140},
  pages={1-26}
}
Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. These measures are exactly the solutions to the q-Pearson equation. In the case of discrete and absolutely continuous measures the difference operator is essentially self-adjoint, and the… CONTINUE READING