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Portraits of frames. (English) Zbl 0851.42030
Summary: We introduce two methods for generating frames of a Hilbert space \(\mathcal H\). The first method uses bounded operators on \(\mathcal H\). The other method uses bounded linear operators on \(l_2\) to generate frames of \(\mathcal H\). We characterize all the mappings that transform frames into other frames. We also show how to construct all frames of a given Hilbert space \(\mathcal H\), starting from any given one. We illustrate the results by giving some examples from multiresolution and wavelet theory.

MSC:
42C15 General harmonic expansions, frames
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