A decomposition theorem for frames and the Feichtinger Conjecture

@inproceedings{Casazza2007ADT,
  title={A decomposition theorem for frames and the Feichtinger Conjecture},
  author={Peter G. Casazza and Gitta Kutyniok and Darrin Speegle and Janet C. Tremain},
  year={2007}
}
In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C*-Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the… 
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20 Citations
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Methods Citations
1
Results Citations
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20 Citations

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TLDR
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The Kadison–Singer Problem in mathematics and engineering
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  • 2006
We will see that the famous intractible 1959 Kadison–Singer Problem in C*-algebras is equivalent to fundamental open problems in a dozen different areas of research in mathematics and engineering.…
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