Abstract
Spectral synthesis deals with the description of translation invariant function spaces on groups. On commutative Abelian groups the basic building bricks of spectral synthesis are the exponential monomials. In this paper we exhibit some methods which can be used to characterize exponential monomials and related function classes using ring-theoretical tools, like modified differences and annihilators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Jacobson, Basic Algebra I, II, W. H. Freeman and Company (New York, 1989).
Laczkovich M., Székelyhidi G.: Harmonic analysis on discrete Abelian groups. Proc. Amer. Math. Soc., 133, 1581–1586 (2005)
M. Laczkovich and L. Székelyhidi, Spectral synthesis on discrete Abelian groups, Math. Proc. Camb. Phil. Soc., 143 (2007), 103–120.
H. Matsumura, Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press (Cambridge, 1989).
L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific Publishing Co. Pte. Ltd. (Singapore, New Jersey, London, Hong Kong, 1991).
L. Székelyhidi, Discrete Spectral Synthesis and Its Applications, Springer Monographs in Mathematics, Springer (Dordrecht, 2006).
L. Székelyhidi, The Levi-Civitá equation vector modules and spectral synthesis, in: Recent Developments in Functional Equations and Inequalities, Banach Center Publications, vol. 99 (2013), pp. 193–206.
L. Székelyhidi, A characterization of exponential polynomials, to appear in Publ. Math. Debrecen.
Author information
Authors and Affiliations
Corresponding author
Additional information
The research was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. NK-81402.
Rights and permissions
About this article
Cite this article
Székelyhidi, L. Annihilator Methods in Discrete Spectral Synthesis. Acta Math. Hungar. 143, 351–366 (2014). https://doi.org/10.1007/s10474-014-0396-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-014-0396-2