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Published July 15, 1998 | Submitted
Journal Article Open

The Classical Moment Problem as a Self-Adjoint Finite Difference Operator

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 Padé 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 Padé approximants for series of Hamburger.

Additional Information

© 1998 Academic Press. Received 13 November 1997, Accepted 3 January 1998. This material is based upon work supported by the National Science Foundation under Grant DMS-9401491.

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