Portraits of frames

Aldroubi, Akram

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

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ISSN 1088-6826(online) ISSN 0002-9939(print)

Portraits of frames

Author: Akram Aldroubi
Journal: Proc. Amer. Math. Soc. 123 (1995), 1661-1668
MSC: Primary 46C05; Secondary 42C15
MathSciNet review: 1242070
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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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