Low-pass filters and representations of the Baumslag Solitar group

Abstract

We analyze representations of solvable Baumslag Solitar group 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 Hausdorff measures.