How to concentrate idempotents
An idempotent is defined as a finite sum \[ f(x)= \exp(2\pi N_1x)+\cdots\exp(2\pi N_mx), \] where \(N_1,\dots, N_m\) are integers. It is said that there holds \(L^p\)-concentration, if there exists a \(c_p> 0\) such that for each interval \(I\subset\mathbb{T}= [-1/2,1/2]\) and each \(\varepsilon> 0\) there exists an idempotent \(f\) such that \[ \Biggl(\int_I |f(x)|^p dx\Biggr)/ \Biggl(\int_{\mathbb{T}} |f(x)|^p dx\Biggr)> c_p- \varepsilon. \] The paper is a survey of results concerning existence of \(L^p\)-concentration for \(p> 0\).
scientific article; zbMATH DE number 5778782
scientific article