Dual generators for weighted irregular wavelet frames and reconstruction error

Dual frames are very useful tools to reconstruct a function and have been explored in many different aspects. In this paper, we give the conditions under which a class of special weighted irregular wavelet frames could have a dual generator with a very explicit form. We also prove that when the irregular translations are changed in some admissible range, the reconstruction formula has a very small perturbation. An example is given to show the use of our main results.