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

摘要

Three well known facts of Fourier series on the disc are extended to Fourier series on the torus, a theorem of Szego, and the fact that any function in H1 can be factored as the product of two functions in H2. 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.