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Polynomially linked additive functions—II.
- Source :
- Aequationes Mathematicae; Jun2018, Vol. 92 Issue 3, p581-597, 17p
- Publication Year :
- 2018
-
Abstract
- We continue the study of additive functions fk:R→F(1≤k≤n)<inline-graphic></inline-graphic> linked by an equation of the form ∑k=1npk(x)fk(qk(x))=0<inline-graphic></inline-graphic>, where the pk<inline-graphic></inline-graphic> and qk<inline-graphic></inline-graphic> are polynomials, R is an integral domain of characteristic 0, and F is the fraction field of R. A method is presented for solving all such equations. We also consider the special case ∑k=1nxmkfk(xjk)=0<inline-graphic></inline-graphic> in which the pk<inline-graphic></inline-graphic> and qk<inline-graphic></inline-graphic> are monomials. In this case we show that if there is no duplication, i.e. if (mk,jk)≠(mp,jp)<inline-graphic></inline-graphic> for k≠p<inline-graphic></inline-graphic>, then each fk<inline-graphic></inline-graphic> is the sum of a linear function and a derivation of order at most n-1<inline-graphic></inline-graphic>. Furthermore, if this functional equation is not homogeneous then the maximal orders of the derivations are reduced in a specified way. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 92
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 129755620
- Full Text :
- https://doi.org/10.1007/s00010-017-0537-0