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Spectral synthesis on discrete Abelian groups

Published online by Cambridge University Press:  01 July 2007

M. LACZKOVICH  and
L. SZÉKELYHIDI
M. LACZKOVICH
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Pázmány Péter sétány 1/C 1117, Hungaryand Department of Mathematics, University College London, Gower Street, London, WC1E 6BT. e-mail: [email protected]
L. SZÉKELYHIDI
Affiliation:
Institute of Mathematics, University of Debrecen, Debrecen, P.O. Box 12, 4010Hungary. e-mail: [email protected]
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Abstract

We prove that spectral synthesis holds on a discrete Abelian group G if and only if the torsion free rank of G is finite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 1 , July 2007 , pp. 103 - 120
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] Á. Bereczky and L. Székelyhidi. Spectral synthesis on torsion groups. J. Math. Anal. Appl. 304 (2005), 607–613.CrossRefGoogle Scholar
[2]Elliot, R. J.. Two notes on spectral synthesis for discrete Abelian groups. Proc. Camb. Phil. Soc. 61 (1965), 617–620.CrossRefGoogle Scholar
[3]Gurevič, D. I.. Counterexamples to a problem of L. Schwartz. Funkcional. Anal. i Priložen 9 (1975), no. 2, 29–35. (English translation: Funkcional Anal. Appl. 9 (1975), no. 2, 116–120.)Google Scholar
[4] J.-P. Kahane. Sur quelques problèmes d'unicité et de prolongement, relatifs aux fonctions approchables par des sommes d'exponentielles. Ann. Inst. Fourier (Grenoble) 5 (1953–54), 39–130.Google Scholar
[5]Kahane, J.-P.. Lectures on Mean Periodic Functions (Tata Institute, 1956).Google Scholar
[6]Kunen, K.. Set Theory (North-Holland, 1980).Google Scholar
[7]Lefranc, M.. Analyse spectrale sur C. R. Paris 246 (1958), 1951–1953.Google Scholar
[8]Ritt, J. F.. Differential Algebra. The American Mathematical Society Colloquium Publications, Vol. 33 (1950).Google Scholar
[9]Rotman, J. J.. An Introduction to the Theory of Groups. Third edition. (Wm. C. Brown Publishers, 1988).Google Scholar
[10]Schwartz, L.. Théorie génerale des fonctions moyenne-périodiques. Ann. of Math. 48 (4) (1947), 857–929.CrossRefGoogle Scholar
[11]Székelyhidi, L.. The failure of spectral synthesis on some types of discrete Abelian groups. J. Math. Anal. Appl. 291 (2004), 757–763.CrossRefGoogle Scholar
[12]Székelyhidi, L.. Polynomial functions and spectral synthesis. Aequationes Math. 70 (1–2), (2005), 122–130.CrossRefGoogle Scholar