Low-pass filters and representations of the Baumslag Solitar group

被引：14

作者：

Dutkay, Dorin Ervin ^{[1
]}

机构：

[1] State Univ New Jersey, Dept Math, Piscataway, NJ 08854 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 358卷 / 12期

关键词：

wavelet; representation; low-pass filter; scaling function; Baumslag Solitar group; solenoid; decomposition; ergodic action; fractal;

D O I：

10.1090/S0002-9947-06-04230-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We analyze representations of the Baumslag Solitar group BS(1, N) = < u, t vertical bar utu(-1) = t(N)> that admit wavelets and show how such representations can be constructed from a given low-pass filter. We describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations. As another application, we construct a Fourier transform for some Hausdor. measures.

引用

页码：5271 / 5291

页数：21

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