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23 April 2024

» arxiv » 1502.5994

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On the equivalence between the sets of the trigonometric polynomials
Krystian Kazaniecki ; Michał Wojciechowski ;
Date:	16 Dec 2014
Abstract:	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 $L^1_Esubset L^1(mathbb{T})$. 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 $d$.
Source:	arXiv, 1502.5994
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