POLYNOMIAL FUNCTIONS AND SPECTRAL SYNTHESIS ON ABELIAN GROUPS

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SZEKELYHIDI LASZLO

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Journal Paper

Paper Information

Journal: BANACH JOURNAL OF MATHEMATICAL ANALYSIS Year:2012 | Volume:6 | Issue:1 Page(s): 124-131

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Title

POLYNOMIAL FUNCTIONS AND SPECTRAL SYNTHESIS ON ABELIAN GROUPS

Author(s)

SZEKELYHIDI LASZLO | Issue Writer Certificate

Keywords

POLYNOMIAL FUNCTION

SPECTRAL SYNTHESIS

NOETHERIAN RING

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.

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APA: Copy

SZEKELYHIDI, LASZLO. (2012). POLYNOMIAL FUNCTIONS AND SPECTRAL SYNTHESIS ON ABELIAN GROUPS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 6(1), 124-131. SID. https://sid.ir/paper/317064/en

Vancouver: Copy

SZEKELYHIDI LASZLO. POLYNOMIAL FUNCTIONS AND SPECTRAL SYNTHESIS ON ABELIAN GROUPS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS[Internet]. 2012;6(1):124-131. Available from: https://sid.ir/paper/317064/en

IEEE: Copy

LASZLO SZEKELYHIDI, “POLYNOMIAL FUNCTIONS AND SPECTRAL SYNTHESIS ON ABELIAN GROUPS,” BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol. 6, no. 1, pp. 124–131, 2012, [Online]. Available: https://sid.ir/paper/317064/en

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