论文标题
有界平均振荡的高斯分析功能
Gaussian analytic functions of bounded mean oscillation
论文作者
论文摘要
我们考虑由带有独立的，中心复杂的高斯系数给出的泰勒序列给出的随机分析功能。我们给出了新的足够条件，以使这种功能具有有限的平均振荡。在轻度的规律性假设下，这种情况是最佳的。使用荷兰和沃尔什的定理，我们作为推论给出了随机高斯汉克尔矩阵的规范的新结合。最后，我们构建了一些特殊的高斯分析功能，这些函数特别反驳了以下猜想，即具有有界平均振荡的随机分析函数始终具有消失的平均振荡。
We consider random analytic functions given by a Taylor series with independent, centered complex Gaussian coefficients. We give a new sufficient condition for such a function to have bounded mean oscillations. Under a mild regularity assumption this condition is optimal. Using a theorem of Holland and Walsh, we give as a corollary a new bound for the norm of a random Gaussian Hankel matrix. Finally, we construct some exceptional Gaussian analytic functions which in particular disprove the conjecture that a random analytic function with bounded mean oscillations always has vanishing mean oscillations.
