[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2021.34.3.271

ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS CORRESPONDING TO POLYNOMIAL SZEGŐ MEASURE WITH AN INFINITE DISCRETE PART

Benghia, Fatima Zohra (Department of Mathematics Laboratory of Pure and Applied Mathematics, Laghouat University)
Belabbaci, Youcef (Department of Mathematics Laboratory of Pure and Applied Mathematics, Laghouat University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.34, no.3, 2021 , pp. 271-283 More about this Journal

Abstract

The asymptotics behavior orthogonal polynomials have been in the spotlight since the result of G. Szegő in 1921. In this paper we study the pointwise asymptotics inside the unit disk for orthogonal polynomials with respect to a polynomial Szegő measure with an infinite masses points.

Keywords

Orthogonal Polynomials; Asymptotics; Polynomial Szego measure; Szego condition; infinite masses points; Hardy space;

Citations & Related Records

Reference

1	V. Kaliaguine and R. Benzine, Sur la formule asymptotique des polynomes orthogonaux associes a une mesure concentree sur un contour plus une partie discrete finie , Bull. Soc. Math. Belg., 41 (1989), 29-46.
2	R. Khaldi and R. Benzine, Asymptotic behavior of orthogonal polynomials corresponding to a measure with infinite discrete part off an arc, Int. J. Math. Math. Sci., 26 (2001), no. 8, 449-455. DOI
3	B. Simon, Orthogonal polynomials on the unit circle. Part 1, American Mathematical Society, Providence, (2005).
4	S. Denisov and S. Kupin, Asymptotics of the orthogonal polynomials for the Szego class with a polynomial weight, J. Approx. Theory., 139 (2006), 8-28. DOI
5	R. Benzine, Asymptotic behavior of orthogonal polynomials corresponding to a measure with infinite discrete part off a curve , Approx. Theory,. 89 (1997), no. 2, 257-265. DOI
6	A. Cachafeiro and F. Marcellan, Perturbation in Toeplitz matrices, J.Math.Anal.Appl., (1991).
7	R. Khaldi and R. Benzine, Asymptotics for orthogonal polynomials off the circle, J. appl. math. phys., 2004 (2004), no. 1, 37-53.
8	R. Khaldi and A. Guezane-Lakoud, Asymptotics of Orthogonal Polynomials With a Generalized Szego Condition, int. J. Open Problems Complex Analysis., 3 (2011) no. 1, ISSN 2074-2827.
9	E. A. Rahmanov, On the asymptotics of the ratio of orthogonal polynomials, II Math. USSD-SB., 46 (1983), 105-117. DOI
10	X. Li and K. Pan, Asymptotic behavior of orthogonal polynomials corresponding to measure with discrete part off the unit circle, J. Aprox. Theory., 79 (1994), 54-71. DOI
11	W. Rudin, Real and Complex Analysis, McGraw-Hill, New York,(1966).
12	G. Szego , Uber die Enttwickelung einer analytischen Funktion nach den poly-nomen einers orthogonal systems, Mathematische zeitchrift, 82 (1921), 188-212.
13	G.Szego, Orthogonal Polynomials, American Mathematical Society, Providence, (1975).