Inverse problems of the scattering by obstacles

在1986年下半年和1987年，我们在几个具体的假设下研究了散射反问题。M. Ikawa获得了关于该检查的结果。我们利用前一年导出的定理将他的结果推广到更一般的情形。这在<section>本基金报告的第3部分中讨论过，该部分是Tsukuba J. Math.11（1987）93- 100中发表的论文的副本。其次，我们精确地研究了散射核在障碍物由两个球组成的情况下的奇异支撑。虽然国外学者开始考虑这类问题，但对这类问题的研究却很少。与N.中村（非成员的这一赠款），我们已经表明如何密切分布的点，这奇异的支持是有关的距离的两个球。这一点在<section>本赠款报告的第2段中有说明。本节是将在日本数学学会杂志40（1988）上发表的论文的副本。

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).