Asymptotic properties of Müntz orthogonal polynomials

Müntz polynomials;Müntz-Legendre polynomials;Asymptotic behavior

Stefánsson, Úlfar F. ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: Müntz polynomials;    Müntz-Legendre polynomials;    Asymptotic behavior;   

Others  :  https://smartech.gatech.edu/bitstream/1853/34759/1/stefansson_ulfar_f_201008_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Müntz polynomials arise from consideration of Müntz's Theorem, which is a beautiful generalization of Weierstrass's Theorem. We prove a new surprisingly simple representation for the Müntz orthogonal polynomials on the interval of orthogonality, and in particular obtain new formulas for some of the classical orthogonal polynomials (e.g. Legendre, Jacobi, Laguerre). This allows us to determine the strong asymptotics and endpoint limit asymptotics on the interval. The zero spacing behavior follows, as well as estimates for the smallest and largest zeros. This is the first time that such asymptotics have been obtained for general Müntz exponents. We also look at the asymptotic behavior outside the interval and the asymptotic properties of the associated Christoffel functions.