MEAN CONVERGENCE OF GENERALIZED JACOBI SERIES AND INTERPOLATING POLYNOMIALS .2.

被引:20
作者
XU, Y [1 ]
机构
[1] UNIV TEXAS, DEPT MATH, AUSTIN, TX 78712 USA
关键词
D O I
10.1006/jath.1994.1006
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Weighted mean convergence of interpolating polynomials based on the zeros of generalized Jacobi polynomials is investigated. The approach is based on generalized Jacobi series and Marcinkiewicz-Zygmund type inequality. © 1994 Academic Press, Inc.
引用
收藏
页码:77 / 92
页数:16
相关论文
共 31 条
[1]   MEAN CONVERGENCE OF ORTHOGONAL SERIES AND LAGRANGE INTERPOLATION [J].
ASKEY, R .
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1972, 23 (1-2) :71-85
[2]  
Ditzian Z., 1987, MODULI SMOOTHNESS
[3]  
Erdos P, 1936, CR HEBD ACAD SCI, V203, P913
[4]   THE BEHAVIOR OF THE DERIVATIVES OF THE ALGEBRAIC POLYNOMIALS OF BEST APPROXIMATION [J].
LEVIATAN, D .
JOURNAL OF APPROXIMATION THEORY, 1982, 35 (02) :169-176
[5]   QUADRATURE SUMS INVOLVING PTH POWERS OF POLYNOMIALS [J].
LUBINSKY, DS ;
MATE, A ;
NEVAI, P .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (02) :531-544
[6]  
Marcinkiewicz J., 1936, STUD MATH, V6, P1
[7]  
MARCINKIEWICZ J., 1937, FUND MATH, V28, P131, DOI DOI 10.4064/FM-28-1-131-166
[8]   NECESSARY CONDITIONS FOR WEIGHTED MEAN CONVERGENCE OF FOURIER-SERIES IN ORTHOGONAL POLYNOMIALS [J].
MATE, A ;
NEVAI, P ;
TOTIK, V .
JOURNAL OF APPROXIMATION THEORY, 1986, 46 (03) :314-322
[9]  
MATE A, 1990, 75TH P ERD BIRTH CEL, P461
[10]  
MUCKENHOUPT B, 1970, T AM MATH SOC, V147, P433, DOI 10.2307/1995205