广义分布空间中卷积算子可解之充要条件

Necessary and Sufficient Conditions for the Convolution Operators to Be Solvable in Generalized Distribution Space

Ｅｈｒｅｎｐｒｅｉｓ及Ｈｏｒｍａｎｄｅｒ在Ｓｃｈｗａｒｔｚ缓增分布空间中讨论了卷积算子的可解。本文充分利用Ｂｅｕｒｌｉｎｇ广义分布空间中的Ｆｏｕｒｉｅｒ－Ｌａｐｌａｃｅ变换的性质，在Ｂｅｕｒｌｉｎｇ广义分布空间中讨论了卷积算子可解的几个等价条件，进而导出了卷积算子可解的充要条件。

Ehrenpreis and Hormander discussed the solvability of convolution operators in Schwartz' space. In this paper,by employing the properties of Fourier-Laplace transform in Beurling's generalized distribution space ,the solvability of convolution operators is discussed and some equivalent conditions for this kind of operators to be solvable are given. Further this paper derives the necessary and sufficient conditions for convolution operators to be solvable ,and extends some results of Hormander's.