The One-Dimensional Hamburger Moment Problem

  • Konrad Schmüdgen
Part of the Graduate Texts in Mathematics book series (GTM, volume 265)


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.


Moment Problem Self-adjoint Extension Theory Weyl Circle Nevanlinna Function Moment Sequence 
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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Konrad Schmüdgen
    • 1
  1. 1.Dept. of MathematicsUniversity of LeipzigLeipzigGermany

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