MUNTZ SYSTEMS AND ORTHOGONAL MUNTZ-LEGENDRE POLYNOMIALS

被引：86

作者：

BORWEIN, P ^{[1
]}

ERDELYI, T ^{[1
]}

ZHANG, J ^{[1
]}

机构：

[1] STANFORD UNIV,DEPT COMP SCI,STANFORD,CA 94305

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 342卷 / 02期

关键词：

EXPONENTIAL POLYNOMIALS; MUNTZ SYSTEMS; MUNTZ-SZASZ THEOREM; MUNTZ-LEGENDRE POLYNOMIALS; RECURRENCE FORMULAS; ORTHOGONAL POLYNOMIALS; CHRISTOFFEL FUNCTIONS; MARKOV-TYPE INEQUALITIES; BERNSTEIN-TYPE INEQUALITIES; NIKOLSKII-TYPE INEQUALITIES; INTERLACING PROPERTIES OF ZEROS; LEXICOGRAPHIC PROPERTIES OF ZEROS;

D O I：

10.2307/2154639

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Muntz-Legendre polynomials arise by orthogonalizing the Muntz system {x(lambda0), x(lambda1), ...} with respect to Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulae for the Muntz-Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros of Laguerre polynomials. The uniform convergence of the Christoffel functions is proved equivalent to the nondenseness of the Muntz space on [0, 1], which implies that in this case the orthogonal Muntz-Legendre polynomials tend to 0 uniformly on closed subintervals of [0, 1). Some inequalities for Muntz polynomials are also investigated, most notably, a sharp L2 Markov inequality is proved.

引用

页码：523 / 542

页数：20

共 27 条

[1] MUNTZ-SZASZ TYPE APPROXIMATION AND ANGULAR GROWTH OF LACUNARY INTEGRAL FUNCTIONS [J].