Parseval p-frames and the Feichtinger conjecture
نویسندگان
چکیده
منابع مشابه
Frames and the Feichtinger Conjecture
We show that the conjectured generalization of the BourgainTzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent sequences. We further show that the two conjectures are impl...
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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 ...
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The constants A and B are called lower and upper frame bounds for the frame. We call a frame {fi}i∈I bounded, if there exists δ > 0 such that ‖fi‖ ≥ δ for all i ∈ I (the norms of the frame elements are always uniformly bounded from above [3, Proposition 4.6]), and unit norm, if ‖fi‖ = 1 for all i ∈ I. If {fi}i∈I is a frame only for its closed linear span, we call it a frame sequence. Those sequ...
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The Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the fi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2015
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2014.11.021