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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access May 31, 2016

Montel–Type Theorems for Exponential Polynomials

  • J. M. Almira EMAIL logo and L. Székelyhidi
From the journal Demonstratio Mathematica


In this paper, we characterize local exponential monomials and polynomials on different types of Abelian groups and we prove Montel-type theorems for these function classes.


[1] J. M. Almira, K. F. Abu-Helaiel, On Montel’s theorem in several variables, Carpathian J. Math. 31 (2015), 1-10. 10.37193/CJM.2015.01.01Search in Google Scholar

[2] J. M. Almira, L. Székelyhidi, Local polynomials and the Montel theorem, Aequationes Math. 89(2) (2015), 329-338.10.1007/s00010-014-0308-0Search in Google Scholar

[3] P. M. Anselone, J. Korevaar, Translation invariant subspaces of finite dimension, Proc. Amer. Math. Soc. 15 (1964), 747-752.10.1090/S0002-9939-1964-0169048-7Search in Google Scholar

[4] D. Z. Djokovic, A representation theorem for (X1 - 1)(X2 - 1) ··· (Xn - 1) and its applications, Ann. Polon. Math. 22 (1969/1970), 189-198.10.4064/ap-22-2-189-198Search in Google Scholar

[5] M. Lefranc, Analyse spectrale sur Zn, C. R. Acad. Sci. Paris 246 (1958), 1951-1953.Search in Google Scholar

[6] L. Székelyhidi, Annihilator methods in discrete spectral synthesis, Acta Math. Hungar. 143(2) (2014), 351-366.10.1007/s10474-014-0396-2Search in Google Scholar

[7] L. Székelyhidi, A characterization of exponential polynomials, Publ. Math. Debrecen 83(4) (2013), 1-17.10.5486/PMD.2013.5768Search in Google Scholar

[8] L. Székelyhidi, On Fréchet’s functional equation, Monatsch. Für Math. 175(4) (2014), 639-643.10.1007/s00605-013-0590-2Search in Google Scholar

[9] L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific, 1991.10.1142/1406Search in Google Scholar

[10] L. Székelyhidi, Polynomial functions and spectral synthesis, Aequationes Math. 70 (2005), 122-130.10.1007/s00010-005-2787-5Search in Google Scholar

[11] L. Székelyhidi, Discrete Spectral Synthesis and its Applications, Springer Monographs in Mathematics, Springer, Dordrecht, 2006.Search in Google Scholar

[12] L. Székelyhidi, Noetherian rings of polynomial functions on Abelian groups, Aequationes Math. 84(1-2) (2012), 41-50.10.1007/s00010-011-0107-9Search in Google Scholar

[13] L. Székelyhidi, Exponential polynomials on commutative hypergroups, Arch. Math. 101(4) (2013), 341-347, to appear.10.1007/s00013-013-0559-3Search in Google Scholar

[14] L. Székelyhidi, Characterization of exponential polynomials on commutative hypergroups, Ann. Funct. Anal. 5(2) (2014), 53-60. 10.15352/afa/1396833502Search in Google Scholar

Received: 2014-7-16
Revised: 2014-12-18
Published Online: 2016-5-31
Published in Print: 2016-6-1

© by J. M. Almira

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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