Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T08:28:14.613Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Lebesgue function of weighted Lagrange interpolation. II

Part of: Approximations and expansions

Published online by Cambridge University Press:  09 April 2009

P. Vértesi
P. Vértesi
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Budapest P.O.B. 127, Hungary, 1364 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this paper is to continue our investigation of the Lebesgue function of weighted Lagrange interpolation by considering Erdős weights on ℝ and weights on [−1, 1]. The main results give lower bounds for the Lebesgue function on large subsets of the relevant domains.

MSC classification

Secondary: 41A05: Interpolation 41A10: Approximation by polynomials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 2 , October 1998 , pp. 145 - 162
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Damelin, S., ‘The Lebesgue function and Lebesgue constant of Lagrange interpolation for Erdős weights’, J. Approx. Theory (to appear).Google Scholar
[2]Damelin, S., ‘Lebesgue bounds for exponential weights on [−1, 1]’, Acta Math. Hungar. (to appear).Google Scholar
[3]Erdős, P. and Turán, P., ‘On interpolation III’, Ann. of Math. 41 (1940), 510–553.CrossRefGoogle Scholar
[4]Levin, A. L. and Lubinsky, D. S., Christoffel functions and orthogonal polynomials for exponential weights on [−1, 1], Mem. Amer. Math. Soc. 535, Vol. 111 (1994).Google Scholar
[5]Levin, A. L. and Lubinsky, D. S. and Mtembu, T. Z., ‘Christoffel functions and orthogonal polynomials for Erdós weights on (−∞, ∞)’, Rend. Mat. Appl. (7) 14 (1994), 199–289.Google Scholar
[6]Lubinsky, D. S., ‘Lx Markov and Bernstein inequalities for Erdós weights’, J. Approx. Theory 60 (1990), 188–230.CrossRefGoogle Scholar
[7]Lubinsky, D. S., ‘An extension of the Erdós-Turán inequality for the sum of successive fundamental polynomials’, Ann. of Numer. Math. 2 (1995), 305–309.Google Scholar
[8]Mastroianni, G. and Russo, M. G., ‘Weighted Lagrange interpolation for Jacobi weights’, Technical Report.Google Scholar
[9]Mastroianni, G. and Totik, V.; ‘Weighted polynomial inequalities with doubling and Ax weights’, J. Approx. Theory (to appear).Google Scholar
[10]Mastroianni, G. and Vértesi, P., ‘Some applications of generalized Jacobi weights’, Acta Math. Hungar. 77, (1997), 323–357.CrossRefGoogle Scholar
[11]Szabados, J., ‘Weighted Lagrange interpolation polynomials’, J. Inequal. Appl. 1 (1997), 99–123.Google Scholar
[12]Szabados, J., ‘Weighted Lagrange and Hermite-Fejér interpolation on the real line’, Technical Report.Google Scholar
[13]Szabados, J. and Vértesi, P., Interpolation of functions (World Scientific, Singapore, New Jersey, London, Hong Kong, 1990).CrossRefGoogle Scholar
[14]PVértesi, , ‘New estimation for the Lebesgue function of Lagrange interpolation’, Acta Math. Acad. Sci. Hungar. 40 (1982), 21–27.CrossRefGoogle Scholar
[15]Vértesi, P., ‘On the Lebesgue function of weighted Lagrange interpolation. I’, Constr. Approx. (to appear).Google Scholar
[16]Vértesi, P., ‘Weighted Lagrange interpolation for generalized Jacobi weights’, Technical Report (to appear).Google Scholar