Portraits of frames

Aldroubi, Akram

doi:10.1090/S0002-9939-1995-1242070-5

Portraits of frames
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by Akram Aldroubi

Proc. Amer. Math. Soc. 123 (1995), 1661-1668

DOI: https://doi.org/10.1090/S0002-9939-1995-1242070-5

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Abstract:

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.

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