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半实轴上带广义Laguerre权的L2空间的精确Jackson不等式
发表时间：2013-01-15 浏览量：2000 下载量：540
| 全部作者： | 孙环，刘永平 |
| 作者单位： | 北京师范大学数学科学学院；江苏省海门中学 |
| 摘 要： | 考虑定义在正半实轴上的函数用n阶代数多项式在加广义Laguerre权的L2-尺度下最佳逼近的精确Jackson不等式。利用该空间定义的熟知广义平移算子和一阶广义连续模，以及广义Laguerre多项式的正交展开式，将待解问题转化为一个具有满足某限定条件的正乘数因子系数的正项级数的极值问题，然后通过对这个极值的适当估计，最终得到用连续模控制最佳逼近的精确常数。 |
| 关 键 词： | 函数逼近；Jackson不等式；半实轴；Laguerre权 |
| Title： | Sharp Jackson inequality in weighted L2-space of half real axis with generalized Laguerre weight |
| Author： | SUN Huan, LIU Yongping |
| Organization： | School of Mathematical Sciences, Beijing Normal University; Haimen Middle School |
| Abstract： | The goal of this article is to consider the precise Jackson inequality of the best approximation of function defined on the positive half axis by algebraic polynomials of n-order in the weighted L2-space with generalized Laguerre weight. Using this well-known generalized translation operator and the generalized modulus of continuity defined in the L2-space of function,and the orthogonal expansion by generalized Laguerre polynomials, the question for solution was transformed into the extremal problem of a set of series with positive terms and some factors of coefficients with imposed restrictions on them. Then through a suitable estimate to this extreme value, the precise constant of the best approximation under the control of the generalized modulus of continuity was obtained finally. |
| Key words： | approximation of function; Jackson inequality; half real axis; Laguerre weight |
| 发表期数： | 2013年1月第1期 |
| 引用格式： | 孙环，刘永平. 半实轴上带广义Laguerre权的L2空间的精确Jackson不等式[J]. 中国科技论文在线精品论文，2013，6（1）：8-15. |
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