follows. In Sec. II we show that the quasi-normal modes are the eigenfunctions of unbounded oscillating regions. As a simple example the quasi-normal modes of a perfectly conducting sphere are considered. The Sec.  III is devoted to the consideration of the quasi-normal modes of a dielectric sphere. The main features of these modes are revealed and their classification is presented. The implication of these quasi-normal modes for estimation of the health hazards of portable telephones is considered in Sec. IV. In Conclusion (Sec. V) the main results are formulated and their relation to the general theory of open systems is discussed.

Quasi-normal modes as the eigenfunctions of unbounded oscillating regions
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Here we show in the general case in what way complex frequencies and quasi-normal modes appear when considering harmonic oscillations in unbounded regions. Let a closed smooth surface $S$ divides the $d$-dimensional Euclidean space $\mathbb{R}^d$ into a compact internal region $D_{\text{ in}}$ and noncompact external region $D_{\text{ex}}$. We consider here a simple scalar wave equation $$\label{2-1} \left ( \Delta -\frac{1}{c^2} \frac{\partial
^2}{\partial t^2} \right )u(t, {\textbf x})=0\,{,}$$ where $c$ is the velocity of oscillation propagation and $\Delta $ is the Laplace operator in $\mathbb{R}^d$. For harmonic oscillations $$\label{2-2} u(t,{\textbf 