平移不变线性算子的连续性Continuity of translation-invariant Linear operators
马米佳
摘要(Abstract)：
利用一类紧ａｂｅｌｉａｎ群Ｇ上的函数空间Ｌ２（Ｇ）上以及 （Ｒ）上平移不变线性泛函的自动连续性并结合闭图象定理证明这些空间上的平移不变线性算子必连续．
关键词(KeyWords)： 平移不变线性泛函;平移不变线性算子;与平移可交换的算子
基金项目(Foundation):
作者(Author): 马米佳
参考文献(References)：
- 1 Meisters GH, Schmidt WH. Translation-invariant linear forms on L2(G) for compact abelian groups G JFunct Anal, 1972. 11: 407~ 424
- 2 Lester CJ. Continuity of operators on L2(G) and L1 (G) commuting with lranslations. J London Math soc,1975. 11 (2): 144~ 146
- 3 Johnson BE. A proof of the translation-invariant form conjecture for L2(G). Bull SC Math, 1983, 107:301 ~ 310
- 4 MeistersGH. Translation-invariant Linear forms and a formula for the Dirac measure. J Funct Anal, 1971,8: 173~ 188
- 5 Meisters GH. Linear operators commuting with franslations on (R) are continuous, Proc AmerMath SOC, 1989, 106: 1079~ 1083
- 6 Rudin W. Functional Analysis. MC Graw-Hill Book Co New York, 1973