Hausdorff's Moment Problem and Expansions in Legendre Polynomials

摘要

A new proof is given for Hausdorff's condition on a set of moments which determines when the function generating these moments is in L2. The proof uses Legendre polynomials and their discrete extensions found by Tchebychef. Then an extension is given to a weighted L2 space using Jacobi polynomials and their discrete extensions. (Author)