The Fréchet Functional Equation for Lie Groups

Molla, Arman; Nicolay, Samuel

doi:10.1007/s00009-021-01701-z

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The Fréchet Functional Equation for Lie Groups

Molla, Arman; Nicolay, Samuel

2021 • In Mediterranean Journal of Mathematics, 18 (2)

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https://hdl.handle.net/2268/257576

DOI
10.1007/s00009-021-01701-z

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Keywords :

Polynomial; Lie group; Functional equation

Abstract :

[en] We study a generalization of the Fréchet functional equation in the setting of Lie groups. We provide theorems that give a description of the solutions and their regularity. These properties are applied to obtain new results about the Fréchet functional equations generalized to homogeneous spaces. In the end, we present a few examples and counterexamples.

Disciplines :

Mathematics

Author, co-author :

Molla, Arman ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

The Fréchet Functional Equation for Lie Groups

Alternative titles :

[en] Belgique

Publication date :

27 February 2021

Journal title :

Mediterranean Journal of Mathematics

ISSN :

1660-5446

eISSN :

1660-5454

Publisher :

Birkhauser Verlag, Switzerland

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Name of the research project :

Generalizations of difference operator and Cauchy functional equations

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 02 March 2021

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Bibliography

Almira, J.M.: Characterization of polynomials as solutions of certain functional equations. J. Math. Anal. Appl. 459, 1016–1028 (2018) DOI: 10.1016/j.jmaa.2017.11.036
Almira, J.M., López-Moreno, A.J.: On solutions of the Fréchet functional equation. J. Math. Anal. Appl. 332, 1119–1133 (2007) DOI: 10.1016/j.jmaa.2006.11.002
Almira, J.M., Shulman, E.V.: On polynomial functions on non-commutative groups. J. Math. Anal. Appl. 458, 875–888 (2018) DOI: 10.1016/j.jmaa.2017.09.020
Almira, J.M., Székelyhidi, L.: Characterization of classes of polynomial functions. Mediterr. J. Math. 13, 301–307 (2016) DOI: 10.1007/s00009-014-0463-5
Boole, G., Moulton, J.F.: A Treatise on the Calculus of Finite Differences, 2nd edn. Dover (1960)
Djoković, D.Ž.: A representation theorem for (x1- 1) (x2- 1).. (xn- 1) and its applications. Ann. Polon. Math. 22, 189–198 (1969)
Fréchet, M.: Une définition fonctionnelle des polynômes. Nouv. Ann. 9, 145–162 (1909)
Fréchet, M.: Les polynômes abstraits. J. Math. Pures Appl. 9(8), 71–92 (1929)
Hamel, G.: Einer Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung f(x+ y) = f(x) + f(y). Math. Ann. 60, 459–472 (1905) DOI: 10.1007/BF01457624
Jordan, C.: Calculus of Finite Differences, 3rd edn. AMS Chelsea Publishing (1965)
Koh, E.L.: The Cauchy functional equation in distribution. Proc. Am. Math. Soc. 106, 641–646 (1989) DOI: 10.1090/S0002-9939-1989-0942634-7
Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities, 2nd edn. Birkhäuser (2009)
Leibman, A.: Polynomial mappings of groups. Israel J. Math. 129, 29–60 (2002) DOI: 10.1007/BF02773152
Millsaps, K.: Abstract polynomials in non-abelian groups. Bull. Am. Math. Soc. 49, 253–257 (1943) DOI: 10.1090/S0002-9904-1943-07891-3
Molla, A., Nicolay, S., Schneiders, J.-P.: On some generalisations of the Fréchet functional equations. J. Math. Anal. Appl. 466, 1400–1409 (2018) DOI: 10.1016/j.jmaa.2018.06.058
Popa, D., Raşa, I.: The Fréchet functional equation with application to the stability of certain operators. J. Approx. Theory 164, 138–144 (2012) DOI: 10.1016/j.jat.2011.09.009
Prager, W., Schwaiger, J.: Generalized polynomials in one and in several variables. Math. Pannon. 20, 189–208 (2009)
Shulman, E.V.: Each semipolynomial on a group is a polynomial. J. Math. Anal. Appl. 479, 765–772 (2019) DOI: 10.1016/j.jmaa.2019.06.050
Stetkær, H.: Functional Equations on Groups. World Scientific, Singapore (2013) DOI: 10.1142/8830
Stetkær, H.: Kannappan’s functional equation on semigroups with involution. Semigroup Forum 94, 17–30 (2017) DOI: 10.1007/s00233-015-9756-7
Székelyhidi, L.: Fréchet’s equation and Hyers theorem on noncommutative semigroups. Ann. Polon. Math. 48, 183–189 (1988) DOI: 10.4064/ap-48-2-183-189
Van der Lijn, G.: La définition fonctionnelle des polynômes dans les groupes abéliens. Fund. Math. 33, 42–50 (1939) DOI: 10.4064/fm-33-1-42-50