We study decoupling theory for functions on $ℝ$ with Fourier transform supported in a neighborhood of short Dirichlet sequences ${\{\log <!--FUNCTION\; APPLICATION-->n\}}_{n=N+1}^{N+N^{1∕2}}$, as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.

中文翻译：

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短广义狄利克雷序列的解耦不等式

我们研究了 $ℝ$ 上函数的解耦理论，并在短狄利克雷序列 ${\{\log <!--FUNCTION\; APPLICATION-->n\}}_{n=N+1}^{N+N^{1∕2}}$ 邻域以及具有类似凸性特性的序列中支持傅里叶变换。我们利用具有接近算术级数的频率支持的函数的波包结构。