Abstract
We extend three well-known facts of Fourier series on the disc to Fourier series on the torus, a theorem of Riesz, a theorem of Szegö, and the fact that any function in H1 can be factored as the product of two functions in H2. Here the rôle of negative integers is played by the lattice points in the third quadrant. In earlier extensions of these theorems this rôle was played by half-planes.
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