Montel-type theorems for exponential polynomials

• Autorzy: Almira, J. M. , Székelyhidi, L.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

PL

wielomiany wykładnicze; twierdzenie Montela

EN

exponential polynomials on Abelian groups; Montel’s theorem

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 2
• Strony: 197--212
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Almira, J. M.

• Depto. Matemáticas. Eps Linares Universidad de Jaén Campus Cientifico Tecnológico de Linares Cinturón Sur S/N 23700 Linares (Jaén), Spain,

autor

Székelyhidi, L.

• Institute of Mathematics University of Debrecen Egyetem Tér 1 4032 Debrecen, Hungary,
• Department of Mathematics University of Botswana 4775 Notwane Rd. Gaborone, Botswana

Bibliografia

• [1] J. M. Almira, K. F. Abu-Helaiel, On Montel’s theorem in several variables, Carpathian J. Math. 31 (2015), 1–10.
• [2] J. M. Almira, L. Székelyhidi, Local polynomials and the Montel theorem, Aequationes Math. 89(2) (2015), 329–338.
• [3] P. M. Anselone, J. Korevaar, Translation invariant subspaces of finite dimension, Proc. Amer. Math. Soc. 15 (1964), 747–752.
• [4] D. Z. Djoković, A representation theorem for (X1 – 1)(X2 - 1)∙∙∙(Xn - 1) and its applications, Ann. Polon. Math. 22 (1969/1970), 189–198.
• [5] M. Lefranc, Analyse spectrale sur Zn, C. R. Acad. Sci. Paris 246 (1958), 1951–1953.
• [6] L. Székelyhidi, Annihilator methods in discrete spectral synthesis, Acta Math. Hungar. 143(2) (2014), 351–366.
• [7] L. Székelyhidi, A characterization of exponential polynomials, Publ. Math. Debrecen 83(4) (2013), 1–17.
• [8] L. Székelyhidi, On Fréchet’s functional equation, Monatsch. Für Math. 175(4) (2014), 639–643.
• [9] L. Székelyhidi, Convolution Type Functional Equations on Topological Abelian Groups, World Scientific, 1991.
• [10] L. Székelyhidi, Polynomial functions and spectral synthesis, Aequationes Math. 70 (2005), 122–130.
• [11] L. Székelyhidi, Discrete Spectral Synthesis and its Applications, Springer Monographs in Mathematics, Springer, Dordrecht, 2006.
• [12] L. Székelyhidi, Noetherian rings of polynomial functions on Abelian groups, Aequationes Math. 84(1–2) (2012), 41–50.
• [13] L. Székelyhidi, Exponential polynomials on commutative hypergroups, Arch. Math. 101(4) (2013), 341–347, to appear.
• [14] L. Székelyhidi,Characterization of exponential polynomials on commutative hypergroups, Ann. Funct. Anal. 5(2) (2014), 53–60.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.