In this article, we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel [1]. Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators (when it exists). The last section of this work is devoted to the properties of the leading eigenvalue (when it exists). So, we discuss the irreducibility of the semigroups generated by these operators. We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

中文翻译：

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具有弹性和非弹性碰撞算子的运输算子的渐近谱

在本文中，我们研究了 Larsen 和 Zweifel [1] 引入的涉及弹性和非弹性碰撞算子的一类中子输运算子的谱特性。我们的分析主要集中在渐近谱的描述上，这在研究由此类算子控制的柯西问题的解的性质时非常有用（当它存在时）。这项工作的最后一部分专门讨论前导特征值的性质（当它存在时）。因此，我们讨论由这些算子生成的半群的不可约性。我们通过讨论相对于算子参数的前导特征值的严格单调性来结束本节。