Memoirs of the American Mathematical Society 2009; 76 pp; softcover Volume: 199 ISBN10: 0821842943 ISBN13: 9780821842942 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/199/933
 This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type is considered which are contained in a given (large) ball and have some additional properties: its connected components have bounded eccentricity, the distances between different connected components are bounded from below, and a uniform `no eclipse condition' is satisfied. It is shown that if an obstacle K in this class has connected components of sufficiently small diameters, then there exists a horizontal strip near the real axis in the complex upper halfplane containing infinitely many scattering resonances (poles of the scattering matrix), i.e. the Modified LaxPhillips Conjecture holds for such K. This generalizes a wellknown result of M. Ikawa concerning balls with the same sufficiently small radius. Table of Contents  Introduction
 An abstract meromorphicity theorem
 Preliminaries
 Ikawa's transfer operator
 Resolvent estimates for transfer operators
 Uniform local meromorphicity
 Proof of the Main Theorem
 Curvature estimates
 Bibliography
