Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Redundancy for localized and Gabor frames   Redundancy is the qualitative property which makes Hilbert space frames so
useful in practice. However, developing a meaningful quantitative notion of
redundancy for infinite frames has proven elusive. Though quantitative
candidates for redundancy exist, the main open problem is whether a frame with
redundancy greater than one contains a subframe with redundancy arbitrarily
close to one. We will answer this question in the affirmative for
$\ell^1$-localized frames. We then specialize our results to Gabor multi-frames
with generators in $M^1(\R^d)$, and Gabor molecules with envelopes in
$W(C,l^1)$. As a main tool in this work, we show there is a universal function
$g(x)$ so that for every $\epsilon>0$, every Parseval frame $\{f_i\}_{i=1}^M$
for an $N$-dimensional Hilbert space $H_N$ has a subset of fewer than
$(1+\epsilon)N$ elements which is a frame for $H_N$ with lower frame bound
$g(\epsilon/(2\frac{M}{N}-1))$. This work provides the first meaningful
quantative notion of redundancy for a large class of infinite frames. In
addition, the results give compelling new evidence in support of a general
definition of reudndancy given in [7].

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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th