关于Malmquist-Takenaka级数的几乎处处收敛性
On almost everywhere convergence of Malmquist-Takenaka series
摘要：
Malmquist-Takenaka系统是经典三角系统的扰动，其中$z$的幂被圆盘的其他默比乌斯变换的乘积所取代。该系统也与所谓的非线性相位解旋分解有内在的联系，该分解一直是最近一些活动的中心。我们证明了$L^p$边界的Malmquist-Takenaka系列的最大部分和算子的默比乌斯变换的零点的额外的假设。我们将问题定位在时间频率设置中，特别是，我们将其连接到多项式Carleson定理。
英文摘要：
The Malmquist-Takenaka system is a perturbation of the classical trigonometric system, where powers of $z$ are replaced by products of other Möbius transforms of the disc. The system is also inherently connected to the so-called nonlinear phase unwinding decomposition which has been in the center of some recent activity. We prove $L^p$ bounds for the maximal partial sum operator of the Malmquist-Takenaka series under additional assumptions on the zeros of the Möbius transforms. We locate the problem in the time-frequency setting and, in particular, we connect it to the polynomial Carleson theorem.
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