FRAME MULTIRESOLUTION ANALYSIS

We generalize bi-orthogonal (non-orthogonal) MAR to frame MRA in which the family of integer translates of a scaling function forms a frame for the initial ladder space . We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there exists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in to be a frame of its closed linear span.