Abstract
Polynomials and exponential polynomials play a fundamental role in the theory of spectral analysis and spectral synthesis on commutative groups. Recently several new results have been published in this field [2–4,6]. Spectral analysis and spectral synthesis has been studied on some types of commutative hypergroups, as well. However, a satisfactory definition of exponential monomials on general commutative hypergroups has not been available so far. In [5,7,8] and [9], the authors use a special concept on polynomial and Sturm–Liouville-hypergroups. Here we give a general definition which covers the known special cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
W. R. Bloom and H. Heyer, Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics, vol. 20, Walter de Gruyter & Co., Berlin, 1995.
M. Laczkovich and G. Székelyhidi, Harmonic analysis on discrete Abelian groups, Proc. Amer. Math. Soc. 133 (2005), 1581–1586.
M. Laczkovich and L. Székelyhidi, Spectral synthesis on discrete Abelian groups, Math. Proc. Camb. Phil. Soc. 143 (2007), 103–120.
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, Spectral analysis and spectral synthesis on polynomial hypergroups, Monatsh. Math. 141 (2004), 33–43.
L. Székelyhidi, Discrete Spectral Synthesis and Its Applications, Springer Monographs in Mathematics, Springer, Dordrecht, The Netherlands, 2006.
L. Székelyhidi, Spectral synthesis on multivariate polynomial hypergroups, Monatsh. Math. 153 (2008), 145–152.
L. Székelyhidi, Functional Equations on Hypergroups, World Scientific Publishing Co. Pte. Ltd., Singapore, New Jersey, London, Hong Kong, 2012.
Vajday L.: Exponential monomials on Sturm-Liouville hypergroups. Banach J. Math. Anal. 4, 139–146 (2010)
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. Exponential polynomials on commutative hypergroups. Arch. Math. 101, 341–347 (2013). https://doi.org/10.1007/s00013-013-0559-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-013-0559-3