Criteria for right disfocality of an \(n\)th order linear difference equation (Q1802713)

The \(n\)th order linear difference equations (1) \(\sum^ n_{i=0}\alpha_ i(m)u(m+i) = 0\), \(m\in I\), is said to be right \(\rho_{\ell}\)-disfocal on \(I^ n\) provided there is no nontrivial solution \(u\) of (1) in \(I \in \{1,2,\dots,n-1\}\). Necessary and sufficient conditions in terms of \(\alpha_ i(m)\) for right \(\rho_ \ell\)-disfocality of (1) together with some special cases are obtained.