linear algebra problem

hi,

i need help with the following problem:

given a sequence x(i,j):Z^2->R, indexed with the 2 dimensional integer grid.

i want to find sequences a(i,j,l), b(i,j,l) :Z^3->R so that x(i,j) can be written as follows:

x(i,j)=\sum_{l\in \mathbb{Z}}a(i,j,l)-a(i,l,j)+b(i,l,j)-
b(l,i,j)

a necessary condition is cleary that

\sum_{i,j}x(i,j) = 0.

is this condition also sufficient?


regards, philipp
.

Quantcast