Fourier monomial on the circle

Summary

The Fourier monomials are the functions $e_n(x) = e^{inx}$, $n \in \Z$, viewed as functions on the circle $\mathbb{T} = \R / 2\pi\Z$. They are the continuous homomorphisms from the circle group to the unit circle of $\C$, that is, the characters of the circle. They form an orthonormal basis of $L^2(\mathbb{T})$, and the coefficients of a function in this basis are its Fourier coefficients.