  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.

Classical Analysis and ODEs;Operator Algebras