Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relevant sampling in finitely generated shift-invariant spaces   We consider random sampling in finitely generated shift-invariant spaces
$V(\Phi) \subset {\rm L}^2(\mathbb{R}^n)$ generated by a vector $\Phi =
(\varphi_1,\ldots,\varphi_r) \in {\rm L}^2(\mathbb{R}^n)^r$. Following the
approach introduced by Bass and Gr\"ochenig, we consider certain relatively
compact subsets $V_{R,\delta}(\Phi)$ of such a space, defined in terms of a
concentration inequality with respect to a cube with side lengths $R$. Under
very mild assumptions on the generators, we show that for $R$ sufficiently
large, taking $O(R^n log(R^{n^2/\alpha'}))$ many random samples (taken
independently uniformly distributed within $C_R$) yields a sampling set for
$V_{R,\delta}(\Phi)$ with high probability. Here $\alpha' \le n$ is a suitable
constant.We give explicit estimates of all involved constants in terms of the
generators $\varphi_1, \ldots, \varphi_r$.

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The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph