Certain linear differential operators and generalized differences

The solution of the problem of finding the quantity
$$ \sup\limits_{|\Delta^ny_k|\le1}\inf\limits_{\substack{f(k)=y_k\\(k=0,\pm1,\pm2,\dots)}}\|f^{(n)}(x)\|_{C(-\infty,\infty)}, $$
obtained by Subbotin, is extended to the case of formally self-adjoint differential operators with constant coefficients and corresponding generalized differences.