作为酉表示的衍射以及测度关于反射Eberlein卷积的正交性
Diffraction as a unitary representation and the orthogonality of measures with respect to the reflected Eberlein convolution
AI总结：
该研究在酉群表示框架下理解平移有界测度的衍射理论，证明了衍射互异测度的正交性，应用于动力系统等领域，并重新证明了纯点衍射的多种特征。
摘要：
我们探讨如何在酉群表示框架下理解单个平移有界测度或此类测度族的衍射理论。这使我们能够证明衍射相互奇异的测度的正交特性。我们将其应用于研究动力系统、精细Eberlein分解，以及相当一般情形下Bombieri--Taylor型结果的有效性。在此过程中，我们还利用我们的方法（重新）证明了纯点衍射的各种特征。
英文摘要：
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures whose diffractions are mutually singular. We apply this to study dynamical systems, the refined Eberlein decomposition and validity of a Bombieri--Taylor type result in a rather general context. Along the way we also use our approach to (re)prove various characterisations of pure point diffraction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
