Characterizing abelian admissible groups
Lehrstuhl A fuer Mathematik, RWTH Aachen
given at strobl11 (15.06.11 16:00)
We consider the question of deciding, for a connected abelian matrix group given in terms of Lie algebra generators, whether the group can serve as a dilation group for a continuous wavelet transform. This amounts to verifying recently established criteria, based on the orbit space of the dual action of the group. The challenge consists in providing explicitly and computationally checkable conditions guaranteeing the existence of a wavelet inversion formula. If the Lie algebra generators have real spectra, these conditions can be described. They do not work, however, for the general case.