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Unbounded Self-adjoint Operators on Hilbert Space pp 363–392Cite as

The One-Dimensional Hamburger Moment Problem

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Part of the book series: Graduate Texts in Mathematics ((GTM,volume 265))

Abstract

In Chap. 16, we present a short and concise treatment of the one-dimensional Hamburger moment problem with an emphasis on the self-adjoint extension theory. Orthogonal polynomials and the Jacobi operator associated with a moment sequence are developed. Basic results on the existence, the set of solutions, and the uniqueness of the moment problem are given in terms of self-adjoint extensions. The two final sections of this chapter are devoted to the advanced theory of the indeterminate case. The four Nevanlinna functions and the Weyl circles are defined and studied, and all von Neumann solutions are described. This chapter ends with a proof of Nevanlinna’s fundamental theorem on the parameterization of the set of all solutions of the indeterminate moment problem.

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  1. Dept. of Mathematics, University of Leipzig, Leipzig, Germany

    Konrad Schmüdgen

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  1. Konrad Schmüdgen
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Schmüdgen, K. (2012). The One-Dimensional Hamburger Moment Problem. In: Unbounded Self-adjoint Operators on Hilbert Space. Graduate Texts in Mathematics, vol 265. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4753-1_16

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