A strong zero theorem for an elliptic equation of high order

In this article we examine a uniformly elliptic equation of high order with simple complex characteristics and with coefficients from $C^1$, defined in a domain $\Omega\subset R^n$ and satisfying there a supplementary condition. At the point $x_0\in\Omega$ let the solution $u(x)$ of this equation have a zero of infinite order. It is shown that then $u\equiv0$ in $\Omega$. Whence a uniqueness theorem is derived for the solution of the Cauchy problem for the equation in question, when the Cauchy data are prescribed on an $(n-1)$-dimensional set of positive measure in the interior of the domain.
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