Portraits of frames

Abstract

We introduce two methods for generating frames of a Hilbert space H \mathcal {H} . The first method uses bounded operators on H \mathcal {H} . The other method uses bounded linear operators on l 2 {l_2} to generate frames of H \mathcal {H} . We characterize all the mappings that transform frames into other frames. We also show how to construct all frames of a given Hilbert space H \mathcal {H} , starting from any given one. We illustrate the results by giving some examples from multiresolution and wavelet theory.