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

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

1999-06-08

arxiv.org/abs/math-ph/9906008v1

Advances in Math. 137 (1998) 82-203

Physics

Mathematical Physics

269K, AMSTeX

Scientific paper

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.

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