一般非均匀凸介质迁移算子本征值的分布

ON THE EIGENVALUE DISTRIBUTION OF THE TRANSPORT OPERATOR FOR NONHOMOGENEOUS CONVEX BODY

本文讨论一般非均匀凸介质所确定的迁移算子的本征值的分布问题，利用Hilbert空间的H算子理论，完整地解决了一般非均匀凸介质中迁移算子本征值的分布问题，若｛｝是迁移算子本征值的一种计数，我们证明了＜＋∞，其中，是粒子的最大逃逸时间，并对本征值的发散程度以及本征值的个数函数作了相应的讨论．

In this paper, we study the eigenvalue distribution problem of the transport operator for nonhomogeneous convex body. By terms of H-operator theory on Hilbert space.We characterized completely the eigenvalue distribution of the transport operator. Let , be an enumeration of eigenvalues of the transport operator, we show: <+∞, where is the maximum escaping time. Moreover, we also discussed the discrete extent of eigenvalues and enumeration function of eigenvalues.