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

Preprint

8 June 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math-ph/9906008

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 Pade 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 Pade approximants for series of Hamburger.

Keywords

FINITE DIFFERENCE OPERATORS
CLASSICAL MOMENT PROBLEM
CONVERGENCE OF PADE
PADE APPROXIMANTS
MOMENT PROBLEM
ADJOINT FINITE

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Version 1, 1999-06-08, ArXiv

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