Abstract
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.
References
[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
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