Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the equivalence between the sets of the trigonometric polynomials   In this paper we construct an injection from the linear space of
trigonometric polynomials defined on $\mathbb{T}^d$ with bounded degrees with
respect to each variable to a suitable linear subspace $L^1_E\subset
L^1(\mathbb{T})$. We give such a quantitative condition on $L^1_E$ that this
injection is a isomorphism of a Banach spaces equipped with $L^1$ norm and the
norm of the isomorphism is independent on the dimension $d$.

1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an