Inverse problems of the scattering by obstacles

在1986年下半年和1987年，我们研究了几种具体假设下的散射逆问题。首先，我们研究了散射矩阵的极点是如何在复平面上分布的。关于这次考试，Ikawa先生得到了一个结果。我们利用我们在前一年推导的定理，把他的结果推广到更一般的情况。这在本次资助报告的b>3部分进行了讨论，该报告是发表在Tsukuba J.Math上的论文的副本。11(1987) 93-100。接下来，我们精确地研究了在障碍物由两个球组成的情况下散射核的奇异支持。这类问题近年来虽有国外学者开始研究，但研究较少。在与N. Nakamura（非该基金成员）的合作中，我们展示了这个单一支撑点的分布与两个球的距离有多么密切的关系。这在本赠款报告的< >2节中有描述。这部分是即将发表在J. Math杂志上的论文的副本。Soc。日本40（1988）。

In the latter half of 1986 and 1987 , we have studied the inverse problems of the scattering under several concrete assumptions.At first, we have examined how the poles of the scattering matrix are distributed in the complex plane. M. Ikawa obtained a result concerning this examination. We have extended his result to more general case by means of the theorems derived by us in the previous year. This is discussed in <section>3 of the report of this grant, which is a copy of the paper published in Tsukuba J.Math. 11 (1987) 93-100.Next, we have examined precisely the singular support of the scattering kernel in the case where the obstacle consists of two balls. Such problems are little studied although some foreign researchers begin to consider them recently. In cooperation with N. Nakamura (non-member of this grant), we have shown how closely the distribution of the points of this singular support is related with the distance of the two balls. This is described in <section>2 of the report of this grant. This section is a copy of the paper which will be published in J. Math. Soc. Japan 40 (1988).