Banach Journal of Mathematical Analysis

Polynomial functions and spectral synthesis on Abelian groups

Laszlo Szekelyhid

Full-text: Open access

Abstract

Spectral synthesis deals with the description of translation invariant function spaces. It turns out that the basic building blocks of this description are the exponential monomials, which are built up from exponential functions and polynomial functions. The author collaborated with Laczkovich [Math. Proc. Cambridge Philos. Soc. 143 (2007), no. 1, 103--120] proved that spectral synthesis holds on an Abelian group if and only if the torsion free rank of the group is finite. The author [Aequationes Math. 70 (2005), no. 1-2, 122--130] showed that the torsion free rank of an Abelian group is strongly related to the properties of polynomial functions on the group. Here we show that spectral synthesis holds on an Abelian group if and only if the ring of polynomial functions on the group is Noetherian.

Article information

Source
Banach J. Math. Anal., Volume 6, Number 1 (2012), 124-131.

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1337014670

Digital Object Identifier
doi:10.15352/bjma/1337014670

Mathematical Reviews number (MathSciNet)
MR2862548

Subjects
Primary: 43A45: Spectral synthesis on groups, semigroups, etc.
Secondary: 39A70: Difference operators [See also 47B39] 16P40: Noetherian rings and modules

Keywords
Polynomial function spectral synthesis Noetherian ring

Citation

Szekelyhid, Laszlo. Polynomial functions and spectral synthesis on Abelian groups. Banach J. Math. Anal. 6 (2012), no. 1, 124--131. doi:10.15352/bjma/1337014670. https://projecteuclid.org/euclid.bjma/1337014670


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