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Two families of compactly supported Parseval framelets in L2(Rd)
Applied and Computational Harmonic Analysis ( IF 2.6 ) Pub Date : 2022-05-13 , DOI: 10.1016/j.acha.2022.04.005
A. San Antolín , R.A. Zalik

For any dilation matrix with integral entries ARd×d, d1, we construct two families of Parseval wavelet frames in L2(Rd). Both families have compact support and any desired number of vanishing moments. The first family has |detA| generators. The second family has any desired degree of regularity. For the members of this family, the number of generators depends on the dilation matrix A and the dimension d, but never exceeds |detA|+d. Our construction involves trigonometric polynomials developed by Heller to obtain refinable functions, the Oblique Extension Principle, and a slight generalization of a theorem of Lai and Stöckler.



中文翻译:

L2(Rd) 中的两个紧支撑 Parseval 框架

对于任何具有整数项的膨胀矩阵一个Rd×d,d1,我们构造了两个 Parseval 小波框架族大号2(Rd). 两个系列都有紧凑的支撑和任意数量的消失时刻。第一个家庭有|检测一个|发电机。第二个家庭有任何想要的规律性。对于这个家族的成员,生成器的数量取决于扩张矩阵A和维度d,但永远不会超过|检测一个|+d. 我们的构造涉及由 Heller 开发的三角多项式以获得可细化函数、斜扩展原理以及 Lai 和 Stöckler 定理的轻微推广。

更新日期:2022-05-13
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