Abstract
In this chapter we begin the study of moment problems using self-adjoint operators and self-adjoint extensions on Hilbert spaces. The operator-theoretic approach is a powerful tool and it will be used in the next two chapters as well.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Berezansky, Y.M.: Expansions in Eigenfunctions of Self-adjoint Operators, Amer. Math. Soc., Providence, R.I., 1968.
Berg, C.: Markov’s theorem revisited, J. Approx. Theory 78(1994), 260–275.
Chihara, T.S.: An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
Derkach, V. A. and M.M. Malamud: The extension theory of hermitian operators and the moment problem, J. Math. Sci. 73(1995), 141–242.
Hamburger, H.L.: Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 81(1920), 235–319, and 82(1920), 120–164, 168–187.
Jones, W.B. and W.J. Thron: Continued Fractions. Analytic Theory and Applications, Addison-Wesley, Reading, Mass., 1980.
Markov, A.A.: Deux demonstrations de la convergence de fractions continues, Acta Math. 19(1895), 235–319.
Rade, L. and B. Westergren: Springers Mathematische Formeln, Springer-Verlag, Berlin, 1991.
Riesz, M.: Sur le problème des moments. Premiere Note. Arkiv för Mat., Astr. och Fysik 16(12) (1921), 23pp.; Deuxieme Note. Arkiv för Mat., Astr. och Fysik 16(19) (1922), 21pp.; Troisieme Note. Arkiv för Mat., Astr. och Fysik 17(12) (1923), 52p.
Schmüdgen, K.: Unbounded Self-adjoint Operators on Hilbert Space, Springer-Verlag, New York, 2012.
Simon, B.: The classical moment problem as a self-adjoint finite difference operator, Adv. Math. 137 (1998), 82–203.
Van Assche, V.: Orthogonal polynomials, associated polynomials and functions of the second kind, J. Comp. Appl. Math. 37(1991), 237–249.
Wall, H.S.: Analytic Theory of Continued Fractions, Amer. Math. Soc., Providence, R.I., 2000.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Schmüdgen, K. (2017). The Operator-Theoretic Approach to the Hamburger Moment Problem. In: The Moment Problem. Graduate Texts in Mathematics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-64546-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-64546-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64545-2
Online ISBN: 978-3-319-64546-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)