Skip to main content
SpringerLink
Log in

Annihilator methods for spectral synthesis on locally compact Abelian groups

Monatshefte für Mathematik Aims and scope Submit manuscript

Cite this article

Abstract

Spectral analysis and spectral synthesis study translation invariant linear function spaces on Abelian groups. Basic function classes for this study are the exponential monomials. These function classes have been investigated on discrete Abelian groups successfully using the annihilator method. In this paper we extend this technique to non-discrete locally compact Abelian groups.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Schwartz, L.: Théorie générale des fonctions moyenne-périodiques. Ann. Math. 48(4), 857–929 (1947)

    Article  MATH  Google Scholar 

  2. Laczkovich, M., Székelyhidi, G.: Harmonic analysis on discrete Abelian groups. Proc. Am. Math. Soc. 133(6), 1581–1586 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Laczkovich, M., Székelyhidi, L.: Spectral synthesis on discrete Abelian groups. Math. Proc. Camb. Phil. Soc. 143(1), 103–120 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Székelyhidi, László: Spectral synthesis problems on locally compact groups. Monatsh. Math. 161(2), 223–232 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Székelyhidi, L.: Annihilator methods in discrete spectral synthesis. Acta Math. Hung. 143(2), 351–366 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Székelyhidi, L.: Harmonic and Spectral Analysis. World Scientific Publishing Co., Pte. Ltd., Hackensack, NJ (2014)

    Book  MATH  Google Scholar 

  8. Kelley, J.L., Namioka, I.: Linear Topological Spaces. Springer, New York (1976)

    MATH  Google Scholar 

  9. Rudin, W.: Fourier Analysis on Groups. Wiley, New York (1990)

    Book  MATH  Google Scholar 

  10. Jacobson, N.: Lectures in Abstract Algebra, vol. II. D. Linear algebra. Van Nostrand Co., Inc, Toronto-New York-London (1953)

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Debrecen, Hungary

    László Székelyhidi

Authors
  1. László Székelyhidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to László Székelyhidi.

Additional information

Communicated by K. Gröchenig.

The research was partly 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. Annihilator methods for spectral synthesis on locally compact Abelian groups. Monatsh Math 180, 357–371 (2016). https://doi.org/10.1007/s00605-015-0822-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-015-0822-8

Keywords

Mathematics Subject Classification

search

Navigation