New characterizations of wavelet frames in

In this paper, the classical problem in frame theory, i.e., characterizing the functions g ∈ L 2 ( R ) and parameters a > 1 , b > 0 such that { D a n T m b g } generates a frame for L 2 ( R ) is discussed. Several new necessary conditions and sufficient conditions are established. We also obtain some new necessary and sufficient conditions under certain assumptions. In particular, we introduce a type of special functions which are similar to Wiener-type functions and use them to characterize wavelet frames.