Polynomial functions on abelian groups are studied from the point of view of spectral synthesis. It is proved that the torsion free rank of an abelian group is finite if and only if each complex generalized polynomial on the group is a polynomial. A conjecture about spectral synthesis on abelian groups is formulated in terms of polynomial functions: spectral synthesis holds on an abelian group if and only if each complex bi-additive function on the group is a bilinear function of complex additive functions.
This is a preview of subscription content,to check access.
Access this article
Similar content being viewed by others
Manuscript received: May 13, 2004 and, in final form, December 5, 2004.
About this article
Cite this article
Székelyhidi, L. Polynomial functions and spectral synthesis. Aequ. math. 70, 122–130 (2005). https://doi.org/10.1007/s00010-005-2787-5