广义函数空间上Drygas型函数方程的稳定性  

Stability of Drygas Functional Equation in Distributions

作　　者：李林松[1] 王丹峰[1] 

机构地区：[1]延边大学理学院数学系,延吉133002

出　　处：《数学的实践与认识》2010年第9期206-213,共8页Mathematics in Practice and Theory

基　　金：教育部回国留学基金(教外司留[2008]890号);吉林省教育厅"十一五"科技项目(自筹)

摘　　要：在广义函数空间上重新定义了Drygas型函数方程的稳定性,然后利用高斯变换将广义函数空间上的函数方程稳定性转换为R^(n+1)空间上的光滑函数方程的稳定性.在求得正则化的函数方程稳定性后,利用广义函数与正则化函数间的关系给出在广义函数空间上的Drygas型函数方程的Hyers-Ulam-Rassias型稳定性.Stability of Drygas＇s functional equation is reformulated in the space of generalized functions, and then by using Gauss transform the stability of functional equation in distributions is converted to usual stability of smooth functional equation on Rn＋1. After the stability of the corresponding regularized functional equation has been solved, the Hyers- Ulam-Rassias stability of Drygas＇s functional equation in the space of generalized functions can also be obtained by the relationship between a generalized function and the regularized function.

关 键 词：热方程的核 广义函数 Drygas函数方程 稳定性 

分 类 号：O174[理学—数学]