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The Operator-Theoretic Approach to the Stieltjes Moment Problem

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Book cover The Moment Problem

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 277))

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Abstract

This chapter is devoted to a detailed study of Stieltjes moment problems by using positive self-adjoint extensions of positive symmetric operators on Hilbert spaces.

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Bibliography

  1. Gebhardt, R.: Das eindimensionale Momentenproblem–Lösungen endlicher Ordnung und das Momentenproblem auf [0, ), Diplomarbeit, Universität Leipzig, 2010.

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  2. Pedersen, H. L.: La parametrisation de Nevanlinna at le problem des moments de Stieltjes indetermine, Expo. Math. 15(1997), 273–278.

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  3. Schmüdgen, K.: Unbounded Self-adjoint Operators on Hilbert Space, Springer-Verlag, New York, 2012.

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  4. Simon, B.: The classical moment problem as a self-adjoint finite difference operator, Adv. Math. 137 (1998), 82–203.

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  5. Stieltjes, T.J.: Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse 8(1894), 1–122, and 9(1895), 1–47.

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Schmüdgen, K. (2017). The Operator-Theoretic Approach to the Stieltjes Moment Problem. In: The Moment Problem. Graduate Texts in Mathematics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-64546-9_8

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