(g*f)(x,y) = \displaystyle \sum_{x \leq z \leq y}f(x,z)g(z,y) = \delta(x,y) \Longrightarrow \\
g(x,x)f(x,x)=1~, ~\forall x \in P$ i $(*)$ $g(x,y)f(x,y)=0~, ~\forall x<y