The discrete Kramer sampling theorem and indeterminate moment problems

摘要

In this paper we propose candidates to be the kernel appearing in the discrete Kramer sampling theorem. These kernels arise either from orthonormal polynomials associated with indeterminate Hamburger or Stieltjes moment problems, or from the second kind orthogonal polynomials associated with the former ones. The sampling points are given by the zeros of the denominator in the Nevanlinna parametrization of the N-extremal measures. Explicit formulae are given associated with some cases where the Nevanlinna parametrization is known explicitly.