[KSCI] Korea Science Citation Index Service

GENERALIZED CHRISTOFFEL FUNCTIONS

Joung, Haewon (Department of mathematics Inha University)

Publication Information

Korean Journal of Mathematics / v.18, no.2, 2010 , pp. 149-160 More about this Journal

Abstract

Let $W(x)={\prod}_{k=1}^m{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$ . Associated with the weight W, upper and lower bounds of the generalized Christoffel functions for generalized nonnegative polynomials are obtained.

Keywords

Christoffel functions; generalized polynomials; Freud weights;

Citations & Related Records

Reference

1	T. Erdelyi, Bernstein and Markov type inequalities for generalized non-negative polynomials, Canad. J. Math. 43(1991), 495-505. DOI
2	T. Erdelyi, Remez-type inequalities on the size of generalized non-negative polynomials, J. Lond. Math. Soc. 45(1992), 255-264. DOI
3	T. Erdelyi, A. Mate, and P. Nevai, Inequalities for generalized nonnegative polynomials, Constr. Approx. 8(1992), 241-255. DOI
4	T. Erdelyi and P. Nevai, Generalized Jacobi weights, Christoffel functions and zeros of orthogonal polynomials, J. Approx. Theory 69(1992), 111-132. DOI
5	G. Freud, On Markov-Bernstein type inequalities and their applications, J. Approx. Theory 19(1977), 22-37. DOI
6	H. Joung, Estimates of Christoffel functions for generalized polynomils with exponential weights, Commun. Korean Math. Soc. 14(1)(1999), 121-134.
7	H. Joung, Infinite finite range inequalities, Korean J. Math. 18(1)(2010), 63-77.
8	A. L. Levin and D. S. Lubinsky, Canonical products and the weights exp ${{\mid}x{\mid}}^\alpha$ ), $\alpha$ > 1, with applications, J. Approx. Theory 49(1987), 149-169. DOI
9	H. N. Mhaskar and E. B. Saff, Where does the Sup Norm of a Weighted Polynomial Live?, Constr. Approx. 1(1985), 71-91. DOI
10	P. Nevai, Bernstein's inequality in $L_p$ for 0 < p < 1, J. Approx. Theory. 27(1979), 239-243. DOI
11	P. Nevai, Geza Freud. Orthogonal Polynomials and Christoffel Functions. A Case Study, J. Approx. Theory. 48(1986), 3-167. DOI
12	P. Nevai, Orthogonal polynomials, Mem. Amer. Math. Soc. 213, 1979.
13	P. Nevai, Polynomials orthonormal on the real line with weight ${{\mid}x{\mid}}^\alpha$ exp(- ${{\mid}x{\mid}}^\beta$ ), I, Acta Math. Hungar. 24(1973), 407-416. DOI