Asymptotic behavior of Müntz-Christoffel functions at the endpoints
The Müntz polynomials have been applied to several problems in approximation theory: a Müntz type of Gauss-Jacobi quadrature has been developed [\textit{G. V. Milovanovic} and \textit{A. S. Cvetkovic, Aleksandar}, SIAM J. Sci. Comput. 27, No.~3, 893--913 (2005; Zbl 1096.41023)] and the zero distribution of the extremal Müntz polynomials has been investigated [\textit{D. S. Lubinsky} and \textit{E. B. Saff}, Proc. Am. Math. Soc. 135, No.~2, 427--435 (2007; Zbl 1173.41001)]. In the paper, the behavior of Cristoffel functions of different Müntz systems for which the respective exponent sequences are asymptotic is compared. More exactly, using the known asymptotics for the ordinary polynomials, the asymptotic behavior of the Cristoffel functions for Müntz systems for which the exponents are asymptotic to an arithmetic progression is established. The fact that the Cristoffel functions can be written in terms of the orthogonal Müntz polynomials is used.
scientific article; zbMATH DE number 5650083