Abstract
We study the asymptotic behavior, as the degree approaches infinity, of the Christoffel function at a fixed point z corresponding to a weight function of the type exp(−|z|λ) on the set |arg z|=π/2+α. The method generalizes that of Rakhmanov and also Mhaskar and Saff.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Landkof, N.S., (1972): Foundations of Modern Potential Theory. Berlin: Springer-Verlag.
Luo, L.S. and J. Nuttall, (1986): Approximation theory and calculation of energies from divergent perturbation series. Phys. Rev. Lett., 57, 2241–2243.
Mhaskar, H.N., E.B. Saff, (1984): Extremal problems for polynomials with exponential weights. Trans.Amer. Math. Soc. 285, 203–234.
Mhaskar, H.N., E.B. Saff, (1985): Where does the sup norm of a weighted polynomial live? Constr. Approx. 1: 71–91.
Moretti, G., (1964): Functions of a Complex Variable. Englewood Cliffs, N.J.: Prentice-Hall.
Muskhelishvili, N.I., (1953): Singular Integral Equations. Groningen: Noordhoff.
Nevai, P.: Geza Freud: Christoffel functions and orthogonal polynomials, J. Approx. Theory, 48, 3–167.
Rakhmanov, E.A., (1984): Asymptotic properties of polynomials orthogonal on the real axis. Math. U.S.S.R. Sbornik, 47, 155–193.
Szegö, G., (1975): Orthogonal Polynomials, Amer. Math. Soc. Colloq. Pub, Vol. 23, Providence: American Mathematical Society.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Luo, L.S., Nuttall, J. (1987). Asymptotic behavior of the Christoffel function related to a certain unbounded set. In: Saff, E.B. (eds) Approximation Theory, Tampa. Lecture Notes in Mathematics, vol 1287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078900
Download citation
DOI: https://doi.org/10.1007/BFb0078900
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18500-0
Online ISBN: 978-3-540-47991-8
eBook Packages: Springer Book Archive