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: 222

Abstract

We investigate the asymptotic behavior of orthogonal polynomials with respect to a measure of the type σ=α+γ, where α is a measure concentrated on a rectifiable Jordan curve and γ is an infinite discrete measure.

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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.

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Published

2007-02-01

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Articles

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