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Extension of three theorems For Fourier series on the disc to the torus

Published online by Cambridge University Press:  17 April 2009

A. G. Miamee
A. G. Miamee
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115-2888, U.S.A.
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 335 - 350
Copyright
Copyright © Australian Mathematical Society 1986

References

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