Regularity of generalized Daubechies wavelets reproducing exponential polynomials with real-valued parameters

We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials with real-valued parameters. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers and Dubuc. The main result is the existence and smoothness of these Daubechies type wavelets.