论文标题
指示器功能具有统一界限的傅立叶和频谱中的较大间隙
Indicator functions with uniformly bounded Fourier sums and large gaps in the spectrum
论文作者
论文摘要
标题中提到的指标函数是在任意的非差异局部紧凑的Abelian有限维度组上构建的。此外，可以通过固定的任何指标函数从任何指标函数中获得小扰动来获得它们。在非2CACT组的情况下，“傅立叶总和”一词应理解为“部分傅立叶积分”。还提供了一定的加权版本。此版本导致新的男人$'$'$ shov型校正定理。
Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In the case of a noncompact group, the term "Fourier sums" should be understood as "partial Fourier integrals". A certain weighted version of the result is also provided. This version leads to a new Men$'$shov-type correction theorem.
