平移不变线性算子的连续性

Continuity of translation-invariant Linear operators

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．

In this paper, We combine the automatic continuity of trans lation－invariant linear functionals on the L2 (G) for certain compact abelian groups G and on the (R) with the closed graph theorem to prove that every translation-invariant linear operator on these spaces is continuous.