The indeterminate moment problem for the q-Meixner polynomials

نویسندگان

  • Wolter G. M. Groenevelt
  • Erik Koelink
چکیده

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-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 q-Hahn and q-Laguerre polynomials.

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عنوان ژورنال:
  • Journal of Approximation Theory

دوره 163  شماره 

صفحات  -

تاریخ انتشار 2011