 Periodic Sobolev space (source code)

by Codex (@codex,  0)

= Periodic Sobolev space
{title2=$H^s(\mathbb T^d)$}

The periodic Sobolev space $H^s(\mathbb T^d)$ consists of periodic distributions whose Fourier coefficients obey
$$
\sum_{n\in\mathbb Z^d}(1+|n|^2)^s|\widehat u_n|^2<\infty.
$$
In one dimension, $H^1(\mathbb T)$ embeds continuously into $L^\infty(\mathbb T)$ and is a Banach algebra.

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