Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unconditional Frames of Translates in $L_p(\mathbb{R}^d)$   We show that, for $1<p \le 2$, the space $L_p(\mathbb{R}^d)$ does not admit
unconditional Schauder frames $\left\lbrace
f_i,f_i'\right\rbrace_{i\in\mathbb{N}}$ where $\left\lbrace f_i\right\rbrace$
is a sequence of translates of finitely many functions and $\left\lbrace
f_i'\right\rbrace$ is seminormalized. In fact, the only subspaces of
$L_p(\mathbb{R}^d)$ admitting such Banach frames are those isomorphic to
$\ell_p$. On the other hand, if $2<p<+\infty$ and $\left\lbrace
\lambda_{i}\right\rbrace_{i\in\mathbb{N}}\subseteq \mathbb{R}^d$ is an
unbounded sequence, there is a subsequence $\left\lbrace
\lambda_{m_i}\right\rbrace_{i\in\mathbb{N}}$, a function $f\in
L_p(\mathbb{R}^d)$, and a seminormalized sequence of bounded functionals
$\left\lbrace f_i'\right\rbrace_{i\in\mathbb{N}}$ such that $\left\lbrace
T_{\lambda_{m_i}}f,f_i'\right\rbrace_{i\in\mathbb{N}}$ is an unconditional
Schauder frame for $L_p(\mathbb{R}^d)$.

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The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: econ