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001-es BibID:	BIBFORM078986
035-os BibID:	(cikkazonosító)74 (WOS)000434419100023 (MR)MR3798020 (Scopus)85046630683
Első szerző:	Gselmann Eszter (matematikus)
Cím:	On functional equations characterizing derivations : methods and examples / Eszter Gselmann, Gergely Kiss, Csaba Vincze
Dátum:	2018
ISSN:	1422-6383 1420-9012
Megjegyzések:	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.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
Megjelenés:	Results in Mathematics. - 73 : 2 (2018), p. 1-23. -
További szerzők:	Kiss Gergely (matematikus) Vincze Csaba (1971-) (matematikus)
Pályázati támogatás:	OTKA K 111651 OTKA ÚNKP-4 Egyéb EFOP-3.6.1-16-2016-00022 EFOP OTKA K 104178 OTKA
Internet cím:	Intézményi repozitóriumban (DEA) tárolt változat DOI
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