# Symbols, Fourier coefficients, and primitive submodules

Would someone please help me to think of examples of functions belonging to the symbol class $S^{1}_{\Lambda}$ introduced at the bottom of page 12 - top of page 13 of http://arxiv.org/pdf/1211.1518.pdf?

The paper is Long-Time Dynamics of Completely Integrable Schrodinger Flows on the Torus, by Anantharaman, Fermanian, and Macia.

I'm especially interested in condition (iii) in the definition of $S^{1}_{\Lambda}$, which restricts the nonzero $x$-Fourier coefficients of elements of the symbol class.

Here, $\Lambda$ is a primitive submodule of the lattice $\mathbb{Z}^d$, and $\langle\Lambda\rangle$ is the real linear span of $\Lambda$.

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