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首页> 外文期刊>Memoirs of the American Mathematical Society >Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture
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Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture

机译：几个小凸体的散射共振和Lax-Phillips猜想

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This work deals with scattering by obstacles which are finite dis-joint unions of strictly convex bodies with smooth boundaries in an odd dimen-sional Euclidean space. The class of obstacles of this type is considered whichare contained in a given (large) ball and have some additional properties:its connected components have bounded eccentricity, the distances betweendifferent connected components are bounded from below, and a uniform 'noeclipse condition' is satisfied. It is shown that if an obstacle K in this classhas connected components of sufficiently small diameters, then there exists ahorizontal strip near the real axis in the complex upper half-plane containinginfinitely many scattering resonances (poles of the scattering matrix), i.e. theModified Lax-Phillips Conjecture holds for such K. This generalizes a well-known result of M. Ikawa concerning balls with the same sufficiently smallradius.
机译：这项工作处理的是障碍物的散射，这些障碍物是在奇维欧几里德空间中具有光滑边界的严格凸体的有限解交合。此类障碍物被认为包含在给定的（大）球中，并且具有一些其他属性：其连接的组件具有有限的偏心率，不同的连接的组件之间的距离从下方限制，并且满足统一的“无月食条件” 。结果表明，如果此类障碍物K的直径足够小，则在复杂上半平面的实轴附近存在水平条带，包含无限多个散射共振（散射矩阵的极点），即修正Lax-菲利普斯猜想适用于这样的K。这概括了Ikawa M.关于半径相同足够小的球的众所周知的结果。

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