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The classical moment problem as a self-adjoint finite difference operator. (English) Zbl 0910.44004

In this comprehensive exposition, the author discusses the classical moment problem from the theory of finite difference operators. The Stieltjes and the Hamburger moment problems are considered from the self-adjointness point of view. As an advantage of this approach it is shown that the Nevanlinna functions appear as elements of a transfer matrix and the convergence of Padé approximants is a strong resolvent convergence of finite matrix approximations to a Jacobi matrix. New results on the convergence of certain Padé approximants for Hamburger series are obtained.

MSC:

44A60 Moment problems
47A57 Linear operator methods in interpolation, moment and extension problems
39A70 Difference operators
41A21 Padé approximation
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