Asymptotic of Lp extremal polynomials off the unit circle

• Autorzy: Khaldi R.
• Języki publikacji: EN

Abstrakty

EN

Let sigma be a positive measure whose support is the unit circle gamma plus a denumerable set of mass points, which accumulate at gamma and satisfy Blaschke^s condition. We study the asymptotics of Lp extremal polynomials (0 < p < oo) in the region exterior to r under Szego's condition.

Słowa kluczowe

EN

extremal polynomials; ortogonal polynomials; asymptotic behavior; unit circle

PL

wielomiany ekstremalne; wielomiany ortogonalne; zachowanie asymptotyczne; rozdział koła

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 3
• Strony: 623--632
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Khaldi R.

• Department of Mathematics, Faculty of Sciences, University Badji Mokhtar, B.P. 12 23000, Annaba, Algeria

Bibliografia

• [1] L. Geronimus, On some extremal problem in L(…) spaces, Math. Sbornik 31 (1952), 3-23 (Russian).
• [2] V. A. Kaliaguine and R. Benzine, Sur la formule asymptotique des polynômes orthogonaux associés à une mesure concentrée sur un contour plus une partie discréte finie, Bull. Soc. Math. Belg., Ser . B 41, (1989), no. 1, 29-46 (French).
• [3] V. A. Kaliaguine, On asymptotics of Lp extremal polynomials on a complex curve (0 < p < ∞), J. Approx. Theory 74 (1993), 226-236.
• [4] R. Khaldi and R. Benzine, On a generalization of an asymptotic formula of orthogonal polynomials, Int. J. Appl. Math. 4 (2000), no. 3, 261-274.
• [5] R. Khaldi and R. Benzine, Asymptotic behavior of class of orthogonal polynomials on the circle: Case of measures with an infinite discrete part. Publications du laboratoire d'analyse numerique et optimisation de Lille I, ANO. no. 411 (2000).
• [6] R. Khaldi and R. Benzine, Asymptotics for orthogonal polynomials off the circle, J. Appl. Math. 1 (2004), 37-53.
• [7] P. P. Korovkine, On orthogonal polynomials on a closed curve, Math. Sbornik 9 (1941), 469-484 (Russian).
• [8] X. Li and K. Pan, Asymptotic, of Lp extremal polynomials on the unit circle, J. Approx. Theory, 67 (1991), 270-283.
• [9] D. S. Lubinsky and E. B. Saff, Strong asymptotics for Lp extremal polynomials (1 < p ≤ ∞) associated with weights on [-1,1], Approximation Theory, Tampa. (Florida, 1985-1986), Lecture Notes in Math., vol. 1287, Springer-Verlag, Berlin (1987), pp. 83-104.
• [10] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1968.
• [11] G. Szegö, Orthogonal Polynomials, 4th ed. American Mathematical Society, Colloquium Publications, vol 23, American Mathematical Society, Rhode Island, 1975.