Extension of Three Theorems of Fourier Series on the Disc to the Torus

摘要

The author extends three well-known facts of Fourier series on the disc to Fourier series on the torus, a theorem of Riesz, a theorem of Szego, and the fact that any function in H sub 1 can be factored as the product of two functions in H sub 2. Here the role of negative integers is played by the lattice points in the third quadrant. In earlier extensions of these theorems this role was played by half-planes. (Author)