Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-15T13:45:42.505Z Has data issue: false hasContentIssue false
  • English
  • Français

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: laczk@cs.elte.hu
L. SZÉKELYHIDI
Affiliation:
Institute of Mathematics, University of Debrecen, Debrecen, P.O. Box 12, 4010Hungary. e-mail: szekely@math.klte.hu
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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