Skip to main content
Log in

On the principal ideal theorem and spectral synthesis on discrete Abelian groups

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We prove a generalization of the discrete version of the Principal Ideal Theorem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Malgrange B.: Equations aux dérivées partielles à coefficients constants. II. Equations avec second membre. C.R. Acad. Sci. Paris 238, 196–198 (1954)

    MathSciNet  MATH  Google Scholar 

  2. Ehrenpreis L.: Mean periodic functions. I. Varieties whose annihilator ideals are principal. Amer. J. Math. 77, 293–328 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lefranc M.: Analyse spectrale sur \({Z_{n}}\). C.R. Acad. Sci. Paris 246, 1951–1953 (1958)

    MathSciNet  MATH  Google Scholar 

  4. Elliott R. J.: Some results in spectral synthesis. Proc. Cambridge Phil. Soc. 61, 395–424 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  5. Elliott R. J.: Two notes on spectral synthesis for discrete Abelian groups. Proc. Cambridge Phil. Soc. 61, 617–620 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gurevič D. I.: Counterexamples to a problem of L. Schwartz. Funkcional. Anal. i Priložen. 9, 29–35 (1975)

    MathSciNet  Google Scholar 

  7. L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific Publishing Co. Inc. (Teaneck, NJ, 1991).

  8. Székelyhidi L.: On the extension of exponential polynomials. Math. Bohemica 125, 365–370 (2000)

    MathSciNet  MATH  Google Scholar 

  9. Székelyhidi L.: The failure of spectral synthesis on some types of discrete abelian groups. J. Math. Anal. Appl. 291, 757–763 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Székelyhidi, Discrete Spectral Synthesis and its Applications, Springer (Dordrecht, 2006).

  11. Laczkovich M., Székelyhidi L.: Spectral synthesis on discrete abelian groups, Math. Proc. Cambridge Phil. Soc. 143, 103–120 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Székelyhidi.

Additional information

The research was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. K111651.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Székelyhidi, L. On the principal ideal theorem and spectral synthesis on discrete Abelian groups. Acta Math. Hungar. 150, 228–233 (2016). https://doi.org/10.1007/s10474-016-0626-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-016-0626-x

Keywords and phrases

Mathematics Subject Classification

Navigation