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arXiv · 1502.05994

On the equivalence between the sets of the trigonometric polynomials

Krystian Kazaniecki·Michał Wojciechowski
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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 $L^1_E\subset L^1(\mathbb{T})$. 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 $d$.

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Krystian Kazaniecki, Michał Wojciechowski. 2014-12-16. On the equivalence between the sets of the trigonometric polynomials. https://arxiv.org/abs/1502.05994

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