On functional equations characterizing derivations: methods and examples

Gselmann, Eszter; Kiss, Gergely; Vincze, Csaba

doi:10.1007/s00025-018-0833-6

Reference : On functional equations characterizing derivations: methods and examples


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/34512

Title :	On functional equations characterizing derivations: methods and examples
Language :	English
Author, co-author :	Gselmann, Eszter []
	Kiss, Gergely [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Vincze, Csaba [University of Debrecen > Geometry]
Publication date :	Jun-2018
Journal title :	Results in Mathematics
Publisher :	Springer
Peer reviewed :	Yes (verified by ORBi^lu)
ISSN :	1422-6383
e-ISSN :	1420-9012
City :	Basel
Country :	Germany
Keywords :	[en] Linear function ; Derivation multiadditive function ; Spectral analysis and synthesis
Abstract :	[en] Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and automorphisms are additive functions satisfying some further functional equations as well. It is an important question that how these morphisms can be characterized among additive mappings in general. The paper contains some multivariate characterizations of higher order derivations. The univariate characterizations are given as consequences by the diagonalization of the multivariate formulas. This method allows us to refine the process of computing the solutions of univariate functional equations of the form ∑k=1nxpkfk(xqk)=0, where pk and qk (k=1,…,n) are given nonnegative integers and the unknown functions f1,…,fn:R→R are supposed to be additive on the ring R. It is illustrated by some explicit examples too. As another application of the multivariate setting we use spectral analysis and spectral synthesis in the space of the additive solutions to prove that it is spanned by differential operators. The results are uniformly based on the investigation of the multivariate version of the functional equations.
Permalink :	http://hdl.handle.net/10993/34512
DOI :	10.1007/s00025-018-0833-6
Other URL :	https://link.springer.com/article/10.1007/s00025-018-0833-6

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