On the equivalence between the sets of the trigonometric polynomials
Abstract
In this paper we construct an injection from the linear space of trigonometric polynomials defined on
T
d
with bounded degrees with respect to each variable to a suitable linear subspace
L
1
E
⊂
L
1
(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
.