On the asymptotics of orthogonal polynomials on the curve with a denumerable mass points

Authors

  • Khaldi Rabah University of Annaba, Algeria
  • Aggoune Fateh University of Annaba, Algeria

DOI:

https://doi.org/10.33993/jnaat361-858

Keywords:

orthogonal polynomials, asymptotic behavior
Abstract views: 192

Abstract

We investigate the asymptotic behavior of orthogonal polynomials with respect to a measure of the type \(\sigma =\alpha +\gamma \), where \(\alpha \) is a measure concentrated on a rectifiable Jordan curve and \(\gamma \) is an infinite discrete measure.

Downloads

Download data is not yet available.

References

Geronimus, L., On some extremal problems in Lσ(p) spaces, Sb. Math., 31, pp. 3-23, 1952.

Kaliaguine, V.A., On asymptotics of L_{p} extremal polynomials on a complex curve (0

https://doi.org/10.1006/jath.1993.1063

DOI: https://doi.org/10.1006/jath.1993.1063

Khaldi, R. and Benzine, R., On a generalization of an asymptotic formula of orthogonal polynomials, Int. J. Appl. Math., 3, pp. 261-274, 2000.

Khaldi, R. and Benzine, R., Asymptotics for orthogonal polynomials off the circle, J. Appl. Math., 1, pp. 37-53, 2004, https://doi.org/10.1155/s1110757x04304092 DOI: https://doi.org/10.1155/S1110757X04304092

Korovkine, P.P., On orthogonal polynomials on a closed curve, Sb. Math., 9, pp. 469-484, 1941.

Li, X. and Pan, K., Asymptotic behavior of class of orthogonal polynomials corresponding to measure with discrete part off the unit circle, J. Approx. Theory, 79, pp. 54-71, 1994, https://doi.org/10.1006/jath.1994.1113 DOI: https://doi.org/10.1006/jath.1994.1113

Rudin, W., Real and complex analysis, McGraw-Hill, New York, 1968.

Stahl, H. and Totik, V., General orthogonal polynomials, Cambridge University Press, 1992, https://doi.org/10.1017/cbo9780511759420 DOI: https://doi.org/10.1017/CBO9780511759420

Szego, G., Orthogonal polynomials, 4th ed. American Mathematical Society, Colloquium Publications, Vol. 23, American Mathematical Society, Rhode Island, 1975.

Downloads

Published

2007-02-01

How to Cite

Rabah, K., & Fateh, A. (2007). On the asymptotics of orthogonal polynomials on the curve with a denumerable mass points. Rev. Anal. Numér. Théor. Approx., 36(1), 89–95. https://doi.org/10.33993/jnaat361-858

Issue

Vol. 36 No. 1 (2007)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.