97-644 Simon B.

The Classical Moment Problem as a Self-Adjoint Finite Difference Operator (269K, AMS-TeX) Dec 22, 97

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Abstract. This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Pad\'e approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we obtain new results on the convergence of certain Pad\'e approximants for series of Hamburger.

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