An Elementary Eigenvalue Criterion for One-Parameter Dilation Groups to   Admit a Continuous Wavelet
  In this article, we present a simple criterion for checking whether a one-parameter matrix group of dilations admits a continuous wavelet. This criterion involves only checking that the eigenvalues of the symmetric part of the matrix have the same sign. In $R^2$ this criterion gives a complete characterization of such matrix groups. 
Netanel Friedenberg, Peter M. Luthy, Guido L. Weiss
math.CA