On the distribution of poles of the scattering matrix for several convex bodies.

*(English)*Zbl 0754.35103
Functional-analytic methods for partial differential equations, Proc. Conf. Symp., Tokyo/Jap. 1989, Lect. Notes Math. 1450, 210-225 (1990).

[For the entire collection see Zbl 0707.00017.]

The author gives a new conjecture concerning the distribution of poles of the scattering matrix associated to an obstacle. This conjecture relies this distribution of poles to the geometry of the obstacle, and modifies the one originally given by Lax and Phillips which is wrong in general. Then the author shows that his conjecture is valid when the obstacle consists in a finite number of small enough balls, with any triad of their centers never lying on a straight line. His proof is based on the study of the zeta function attached to the obstacle, and on a result concerning singular perturbations of symbolic flows.

The author gives a new conjecture concerning the distribution of poles of the scattering matrix associated to an obstacle. This conjecture relies this distribution of poles to the geometry of the obstacle, and modifies the one originally given by Lax and Phillips which is wrong in general. Then the author shows that his conjecture is valid when the obstacle consists in a finite number of small enough balls, with any triad of their centers never lying on a straight line. His proof is based on the study of the zeta function attached to the obstacle, and on a result concerning singular perturbations of symbolic flows.

Reviewer: A.Martinez (Villetaneuse)