Polynomial wavelets construction using generalized coherent states

This paper aimed to investigate the relation between the coherent states and the wavelets. So first the standard، generalized and nonlinear coherent states were reviewed and then their properties were presented. As an example of the nonlinear coherent states، the coherent states of a two-dimensional harmonic oscillator on a flat space were examined. Using the Dirac notation، the admissibility condition of the mother wavelets was studied. Then by means of the resolution of the identity of the generalized coherent states and the admissibility condition of the wavelets، a systematic method was presented to calculate the polynomial wavelets. At the end، as an illustrative example، the polynomial wavelets were constructed by using the nonlinear coherent states on a flat space.