| 用非标准离散函数和差商定义新广义函数 |
| |
| 引用本文： | 李邦河,李雅卿.用非标准离散函数和差商定义新广义函数[J].应用泛函分析学报,2004,6(4):322-346. |
| |
| 作者姓名： | 李邦河 李雅卿 |
| |
| 作者单位： | 中国科学院数学与系统科学研究院,北京,100080 |
| |
| 基金项目： | Project supported by the National Natural Science Foundation of China(G19990 75 10 4 ) |
| |
| 摘 要： | 在非标准分析框架下，用离散函数定义新广义函数，用差商定义其导数．对Schwartz广义函数以及更广的Gevrey超广义函数，文章证明了广义导数可以用差商表示．此外还给出了此新广义函数和Sobolev理论的关系．
|
| 关 键 词： | 广义函数 差商 导数 非标准分析 表示 证明 框架 |
Defining New Generalized Functions by Nonstandard Discrete Functions and Difference Quotients |
| |
| LI Bang-he,LI Ya-qing.Defining New Generalized Functions by Nonstandard Discrete Functions and Difference Quotients[J].Acta Analysis Functionalis Applicata,2004,6(4):322-346. |
| |
| Authors: | LI Bang-he LI Ya-qing |
| |
| Institution: | LI Bang-he,LI Ya-qing Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China |
| |
| Abstract: | By using nonstandard analysis, we define new generalized functions as discrete functions, and their derivatives are defined as difference quotients. For Gevrey's ultradistributions, including Schwartz'distributions, we prove that difference quotients are indeed good replacements of generalized derivatives. Relatoions of our new generalized functions with Sobolev theory are presented. It is expected that this theory will be useful for nonlinear partial differential equations with distributional data, via difference method. |
| |
| Keywords: | nonstandard analysis difference methord discrete functional analysis new generalized function distribution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
