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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 3, Pages 441-457
http://dx.doi.org/10.1155/S016117128200043X

Second degree polynomials and the fundamental theorems of harmonic analysis

Department of Pure and Applied Mathematics, Washington State University, Pullman 99164, Washington, USA

Received 11 September 1981

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The concept of a second degree polynomial with nonzero subdegree is investigated for Abelian groups, and it is shown how such polynomials can be exploited to produce elementary proofs for the Uniqueness Theorem and the Fourier Inversion Theorem in abstract harmonic analysis.