论文标题
关于复杂的分析工具和全态旋转方法
On Complex Analytic tools, and the Holomorphic Rotation methods
论文作者
论文摘要
我们描述了上半平面中强烈空间的经典环境中的最新非线性分析近似工具，并显示了如何将它们传递到上半空间中谐波函数的更高维真实设置。众所周知，[6]，较高维度的所有谐波函数都是在2维平面上塑形函数的组合，在正常方向上延伸为恒定。我们得出具有相应异构体的表示定理，为高度振荡性多维信号的处理打开了大门。
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It is known [6] that all harmonic functions in higher dimensions are combinations of holomorphic functions on 2 dimensional planes, extended as, constant in normal directions. We derive representation theorems, with corresponding isometries, opening the door for applications in higher dimensions, to the processing of highly oscillatory multidimensional signals.
