On the application of spectral theory to obtain estimates of solutions of the Schrödinger equation

Estimates which depend on the lower bound $M$ of the minimal operator $-\Delta+q$, $\operatorname{Im}q=0$ in the neighborhood of the point $x$ are obtained for the solutions $u(x)$ of the Schrödinger equation. The behavior of $u(x)$ as $|x|\to\infty$ in a cone, and in the whole of $\mathbf R^n$, is investigated in the case $M>0$.
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