Heisenberg群上的Mexican Hat小波
Mexican Hat Wavelet on the Heisenberg Group
摘要：
本文从Calderon公式的角度研究了Heisenberg群上的小波（容许向量）。此外，我们将表明，类施瓦茨功能的卡尔德龙容许条件是等价的，通常的容许属性，将在这项工作中介绍。此外，激发一个著名的例子在实数线，墨西哥帽小波，我们证明了存在和建设的海森堡李群上的类似小波2消失的时刻，连同其所有的衍生物具有高斯衰减。
英文摘要：
In this article wavelets (admissible vectors) on the Heisenberg group are studied from the point of view of Calderon's formula. Further we shall show that for the class of Schwartz functions the Calderon admissibility condition is equivalent to the usual admissibility property which will be introduced in this work. Furthermore motivated by a well-known example on the real line, the Mexican-Hat wavelet, we demonstrate the existence and construction of an analogous wavelet on the Heisenberg Lie group with 2 vanishing moments, which together with all of its derivatives has Gaussian decay.
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