Kernels of higher order Cauchy differences on free groups
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| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0325-z |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0325-z | ||
| 100 | 1 | |a Ng |D Che |u Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, Canada |4 aut | |
| 245 | 1 | 0 | |a Kernels of higher order Cauchy differences on free groups |h [Elektronische Daten] |c [Che Ng] |
| 520 | 3 | |a Let (G, .) be a group, (H, +) an abelian group and f : G → H. The first and the second Cauchy differences of f are $$\begin{aligned} & \quad C^{1}f(x,y) = f(xy) - f(x) - f(y), \\ & C^{2}f(x,y,z) = f(xyz) - f(xy) - f(yz) - f(xz) + f(x) + f(y) + f(z).\end{aligned}$$ C 1 f ( x , y ) = f ( x y ) - f ( x ) - f ( y ) , C 2 f ( x , y , z ) = f ( x y z ) - f ( x y ) - f ( y z ) - f ( x z ) + f ( x ) + f ( y ) + f ( z ) . Higher order Cauchy differences $${C^{m}f}$$ C m f are defined recursively. The functional equation $$C^{m}f = 0$$ C m f = 0 is studied. Some earlier results on the equation $${C^{2}f = 0}$$ 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. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Functional equations |2 nationallicence | |
| 690 | 7 | |a free groups |2 nationallicence | |
| 690 | 7 | |a Cauchy differences |2 nationallicence | |
| 690 | 7 | |a finite differences |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 119-147 |x 0001-9054 |q 89:1<119 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0325-z |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0325-z |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Ng |D Che |u Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, ON, Canada |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 119-147 |x 0001-9054 |q 89:1<119 |1 2015 |2 89 |o 10 | ||