The Classical Moment Problem as a Self-Adjoint Finite Difference Operator
Copyright policy )The Classical Moment Problem as a Self-Adjoint Finite Difference Operator
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.
269K, AMSTeX
- Division of Physics United States
- California Institute of Technology United States
- Directorate for Mathematical & Physical Sciences United States
Mathematics(all), convergence, self-adjoint finite difference operator, FOS: Physical sciences, Mathematical Physics (math-ph), Hamburger series, 620, 510, Hamburger moment problem, Moment problems, Padé approximants, Nevanlinna functions, Stieltjes moment problem, Difference operators, Linear operator methods in interpolation, moment and extension problems, Padé approximation, Mathematical Physics
Mathematics(all), convergence, self-adjoint finite difference operator, FOS: Physical sciences, Mathematical Physics (math-ph), Hamburger series, 620, 510, Hamburger moment problem, Moment problems, Padé approximants, Nevanlinna functions, Stieltjes moment problem, Difference operators, Linear operator methods in interpolation, moment and extension problems, Padé approximation, Mathematical Physics
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