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

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Abstract

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

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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 

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, H-4010, Debrecen, Hungary

    L. Székelyhidi

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  1. L. Székelyhidi
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Correspondence to L. Székelyhidi.

Additional information

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

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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

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

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