The indeterminate moment problem for the q-Meixner polynomials

作者：Groenevelt Wolter^*; Koelink Erik

来源：Journal of Approximation Theory, 2011, 163(7): 838-863.

DOI：10.1016/j.jat.2010.07.001

• Indeterminate moment problem
• Orthogonal polynomials
• q-Meixner polynomials

For a class of orthogonal polynomials related to the q-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal polynomials to an orthogonal basis for the corresponding weighted L(2)-space explicitly. The result is proved in two ways; by a spectral decomposition of a suitable operator and by direct series manipulation. We discuss extensions to explicit non-positive measures and the relation to other indeterminate moment problems for the continuous dual q(-1)-Hahn and q-Laguerre polynomials.

• 出版日期2011-7