  Consider the solution of the time-dependent Schr{\"o}dinger equation with
initial data $f$. It is shown in \cite{artikel} that there exists $f$ in the
Sobolev space $H^s(\RR), s=n/2$ such that tangential convergence can not be
widened to convergence regions. In this paper we show that the corresponding
result holds when $-\Delta_x$ is replaced by an operator $\phi(D)$, with
special conditions on $\phi$.
