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Proceedings of the American Mathematical Society

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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Keywords: Frames, frame-preserving mappings, affine frames, multiresolution, wavelets
Article copyright: © Copyright 1995 American Mathematical Society