Abstract
This study is concerned with the uncertainty principles which are related to the Weyl-Heisenberg, the SIM(2) and the Affine groups. A general theorem which associates an uncertainty principle to a pair of self-adjoint operators was previously used in finding the minimizers of the uncertainty principles related to various groups, e.g., the one and two-dimensional Weyl-Heisenberg groups, the one-dimensional Affine group, and the two-dimensional similitude group of ℝ2, SIM(2) = ℝ2 ×(ℝ+ × SO(2)). In this study the relationship between the affine group in two dimensions and the SIM(2) group is investigated in terms of the uncertainty minimizers. Moreover, we present scale space properties of a minimizer of the SIM(2) group.
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