Abstract
In the preceding chapters we derived basic existence and uniqueness results for moment problems. In this chapter we develop two powerful tools for a “finer” study of one-dimensional moment problems: orthogonal polynomials and Jacobi operators.
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
Chihara, T.S.: An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
Dunkl, C.F. and Y. Xu: Orthognal Polynomials of Several Variables, Cambridge Univ. Press, Cambridge, 2001.
Favard, J.: Sur le polynomes de Tchebycheff, C. R. Acad. Sci. Paris 200(1935), 2052–2055.
Heine, E.: Handbuch der Kugelfunktionen. Theorie und Anwendungen, Vols. 1 and 2, G. Reimer, Berlin, 1878 and 1881.
Ismail, M.E.H.: Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge Univ. Press, Cambridge, 2004.
Marcellan, F. and R. Alvarez-Nodarse: On the “Favard theorem” and its extension, J. Comput. Appl. Math. 37(2001), 213–254.
Rade, L. and B. Westergren: Springers Mathematische Formeln, Springer-Verlag, Berlin, 1991.
Simon, B.: Orthogonal Polynomials on the Unit Circle, Part I: Classical Theory, Amer. Math. Soc., Providence, R.I., 2005.
Simon, B.: Szegö’s Theorem and Its Descendants, Princeton Univ. Press, Princeton, 2011.
Szegö, G.: Orthogonal Polynomials, Amer. Math. Soc., Providence, R.I., 1939.
Wendroff, B.: On orthogonal polynomials, Proc. Amer. Math. Soc. 12(1961), 554–555.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Schmüdgen, K. (2017). Orthogonal Polynomials and Jacobi Operators. In: The Moment Problem. Graduate Texts in Mathematics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-64546-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-64546-9_5
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)