摘要
设整数1≤j<m≤n.范数‖.‖ωthe norm‖f‖2ω=∫1-1f2(x)ω(x)dx.首先讨论了一个关于正交的Chebyshev多项式Tn(x)的Kolmogoroff型不等式.利用Tn(x)的正交性,对满足条件的整数的j和m,建立了代数多项式pn(x)的加权Kolmogoroff型不等式:‖(1-x2)jp(nj)(x)‖2ωT≤ajm‖(1-x2)mp(n m)(x)‖2ωT+bjm‖pn(x)‖2ωT对任意的pn(x)∈πn成立(πn为次数不超过n的代数多项式空间),并且指出其不等式的系数在某种意义上是最好可能的.
Let 1≤jm≤n be integers.Denote by ‖·‖ω the norm ‖f‖ω^2=∫-1^1f^ 2（x）ω（x）dx.Begins with a discussion of the Kolmogoroff type inequalities for orthogonal Chebyshev polynomial Tn（x）.Make full use of orthogonal nature of the Tn（x）,we establish weighted Kolmogoroff Type Inequality of algebraic polynomials pn（x） for eligible integers of j and m ‖√1-x^2）jpn^（j）（x）‖ωT^2≤ajm‖√1-x^2）^mpn^（m）（x）‖ωT^2＋bjm‖pn^（x）‖ωT^2 which hold for every pn（x）∈πn（πn denotes the space of real algebraic polynomials of degree not exceeding n）,and the coefficients in our inequality is the best possible in some sense.
出处
《浙江水利水电专科学校学报》
2010年第3期89-92,共4页
Journal of Zhejiang Water Conservancy and Hydropower College
基金
浙江省教育厅科研基金(20054080)
