The affine Wigner distribution

We examine the affine Wigner distribution from a quantization perspective with an emphasis on underlying group structure. One of our main results expresses scalogram as (affine) convolution distributions. strive to unite literature distributions and we provide connection Mellin transform in rigorous manner. Moreover, present ambiguity function show how this can be used illuminate properties distribution. In contrast usual distribution, demonstrate that is never analytic function. Our approach naturally leads several applications, one which approximation problem for deviation symbol expressed purely terms intrinsic operator-related symbol. Finally, positivity conjecture regarding non-negativity