New characterizations of wavelet frames in L2(R)L2(R)

In this paper, the classical problem in frame theory, i.e., characterizing the functions g∈L2(R)g∈L2(R) and parameters a>1,b>0a>1,b>0 such that {DanTmbg}{DanTmbg} generates a frame for L2(R)L2(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.