论文标题
纯点衍射和平均值，besicovitch和Weyl几乎是周期性
Pure Point Diffraction and Mean, Besicovitch and Weyl Almost Periodicity
论文作者
论文摘要
我们表明，当且仅当它平均几乎是周期性时，翻译有限的度量具有纯点衍射。然后，我们继续表明，当且仅当它是besicovitch几乎是周期性的情况下，翻译有限的措施就解决了我们所说的相位问题。最后，我们表明，当且仅当它是Weyl几乎是周期性的时，翻译有限的度量与基础范霍夫序列无关。这些结果解决了纯点衍射理论中的基本问题，并回答了拉加里亚斯的问题。
We show that a translation bounded measure has pure point diffraction if and only if it is mean almost periodic. We then go on and show that a translation bounded measure solves what we call the phase problem if and only if it is Besicovitch almost periodic. Finally, we show that a translation bounded measure solves the phase problem independent of the underlying van Hove sequence if and only if it is Weyl almost periodic. These results solve fundamental issues in the theory of pure point diffraction and answer questions of Lagarias.
