Characterization of scaling functions

We give a complete characterization of functions � 2 L 2 (R n ), which generate frame multiresolution analyses. The char- acterization of scaling functions of a multiresolution analysis is de- duced from the main result. The fact that in the closed linear span of translates of a single function there exists a tight frame permits us to obtain the characterization of scaling functions for more general cases from our main result.