论文标题
LCA组的傅立叶可转换度量的唯一定理
Uniqueness theorem for Fourier transformable measures on LCA groups
论文作者
论文摘要
我们表明，如果两个离散的“不太厚”的LCA组的傅立叶傅立叶可转换度量的支撑点趋向于无穷大，而在这些点上的质量也是如此，那么这些度量是重合的。结果也适用于LCA组的几乎定期措施有效。另外，我们表明，对于某些离散的“厚”措施，结果是错误的。为此，我们在真实轴上构建了一个离散的几乎周期性度量，随着这些点接近无穷大，其支撑点的质量往往为零。
We show that if points of supports of two discrete "not very thick" Fourier transformable measures on LCA groups tend to one another at infinity and the same is true for the masses at these points, then these measures coincide. The result is valid for discrete almost periodic measures on LCA groups too. Also, we show that the result is false for some discrete "thick" measures. To do this, we construct a discrete almost periodic measure on the real axis, whose masses at the points of support tend to zero as these points approach infinity.
