论文标题
具有算术频谱的措施的Hausdorff尺寸
Hausdorff dimension of measures with arithmetically restricted spectrum
论文作者
论文摘要
我们根据其光谱的算术特性，从下面提供了单位圆的较低措施的估计值。我们通过应用一般结果来获得我们的界限，用于$ q $ gundales to gundy-varopoulos向后的martingale。为了显示我们方法的清晰度，我们改善了某些Riesz产品的Hausdorff尺寸的最著名的数值下限。
We provide an estimate from below for the lower Hausdorff dimension of measures on the unit circle based on the arithmetic properties of their spectra. We obtain our bounds via application of a general result for abstract $q$-regular martingales to the Gundy--Varopoulos backwards martingale. To show the sharpness of our method, we improve the best known numerical lower bound for the Hausdorff dimension of certain Riesz products.
