Some Extremal Problems for Algebraic Polynomials in Loaded Spaces

被引：2
作者：
Osilenker, B. P. [1 ]
机构：
[1] Moscow State Bldg Univ, Yaroslavskoe Sh 26, Moscow 129337, Russia
来源：
RUSSIAN MATHEMATICS | 2010年 / 54卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
extremal problem; loaded spaces; loaded orthogonal polynomials; algebraic polynomials; classical Jacobi polynomials;
D O I：
10.3103/S1066369X10020064
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a loaded Jacobi space with the inner product < f, g > = Gamma(alpha + beta + 2)/2(alpha+beta+1)Gamma(alpha+1)Gamma(beta+1) integral(1)(-1) fg(1-x)(alpha)(1+ x)(beta)dx+Lf(1)g(1)+Mf(-1)g(-1) (L, M >= 0) we consider the lth derivative of the algebraic polynomial Pi((r))(N)(x) = Sigma(N)(k=N-r+1) a(k)((0)) x(k) + Sigma(N-r)(j=0) a(j)x(j) (a(N)((0)) > 0) with fixed coefficients a(k)((0)). We solve the following extremal problems: Find inf < D-l[Pi((r))(N) (x)], D-l[Pi((r))(N) (x)]> (D = d/dx, 0 <= l <= N - r) and calculate extremal polynomials.
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页码：46 / 56
页数：11
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