Necessary conditions for the stability of difference schemes

For difference equations of the form $u^{n+1}=Au^n+f^nh$, $n\le T/h$ the necessary condition for stability due to von Neumann is well known; this condition is expressed in terms of the spectrum of the operator $A$: $r(A)\le1+ch$. In this note, for a certain class of difference equations, we express this condition in terms of the spectral radius of the symbol of the operator $A$.