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 , , we construct two families of Parseval wavelet frames in . Both families have compact support and any desired number of vanishing moments. The first family has 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 . 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,,我们构造了两个 Parseval 小波框架族. 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. 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。