论文标题
$ l^1 $ -FLAT多项式和简单的保守地图频谱：一个简单的证明
$L^1$-flat polynomials and simple Lebesgue spectrum for conservative maps exist: A simple proof
论文作者
论文摘要
我们提供了一个简单的证明，证明了$ l^1 $ -FLAT分析多项式具有系数$ 0,1 $在圆圈和真实的行中，我们给出了一个保守的Ergodic地图和流程的示例，其统一操作员承认一个简单的Lebesgue Spectrum。除其他结果外，我们还可以回答波尔加因关于$ l^1 $ norm nors of topernomials的问题的答案，以及受到莱默（Lehmer）问题启发的问题，这是对这些多项式量的Mahler量度的启发。
We present a simple proof on the existence of $L^1$-flat analytic polynomials with coefficients $0,1$ on the circle and on the real line and we give an example of a conservative ergodic map and flow whose unitary operators admits a simple Lebesgue spectrum. Among other results, we obtain an answer to Bourgain's question on the supremum of $L^1$-norm of such polynomials and to a question inspired by Lehmer's problem on the supremum of the Mahler measures of those polynomials.
