Kernel of the second order Cauchy difference on groups |
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| Authors: | Che Tat Ng Hou Yu Zhao |
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| Affiliation: | 1. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
2. School of Mathematics, Chongqing Normal University, Chongqing, 401331, People’s Republic of China
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| Abstract: | Let (G, ·) be a group, (H, +) be an abelian group, and ${f:Grightarrow H}$ . The second order Cauchy difference of f is $$C^{(2)}f(x,y,z)=f(xyz)-f(xy)-f(yz)-f(xz)+f(x)+f(y)+f(z).$$ The functional equation $$C^{(2)}f(x,y,z)=0$$ is studied. We present its general solution on free groups. Solutions on other selected groups are also given. |
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