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- Title
Kernels of higher order Cauchy differences on free groups.
- Authors
Ng, Che
- Abstract
Let ( G, .) be a group, ( H, +) an abelian group and f : G → H. The first and the second Cauchy differences of f are Higher order Cauchy differences $${C^{m}f}$$ are defined recursively. The functional equation is studied. Some earlier results on the equation $${C^{2}f = 0}$$ are extended to higher m. For m = 3 we present its general solution on free groups G. When the free group has just one generator the solution is obtained for all m.
- Subjects
KERNEL (Mathematics); FREE groups; MATHEMATICAL functions; GROUP theory; KERNEL functions; CAUCHY problem; FINITE differences
- Publication
Aequationes Mathematicae, 2015, Vol 89, Issue 1, p119
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-014-0325-z