Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and Tiling properties of the Unit Cube   Let $\Q=[0,1)^d$ denote the unit cube in $d$-dimensional Euclidean space \Rd
and let \T be a discrete subset of \Rd. We show that the exponentials
$e_t(x):=exp(i2\pi tx)$, $t\in\T$ form an othonormal basis for $L^2(\Q)$ if and
only if the translates $\Q+t$, $t\in\T$ form a tiling of \Rd.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph