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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Portraits of frames
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by Akram Aldroubi PDF
Proc. Amer. Math. Soc. 123 (1995), 1661-1668 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1661-1668
  • MSC: Primary 46C05; Secondary 42C15
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242070-5
  • MathSciNet review: 1242070