具各向异性散射和裂变的迁移算子本征值的分布

On the Eigenvalue Distribution of the transport Operator for Anisotropic Scattering and Fission

对一般具各向异性、连续能量、非均匀凸介质所确定的迁移算子，利用Ｈｉｌｂｅｒｔ空间的Ｈｉｌｂｅｒｔ－Ｓｃｈｍｉｄｔ算子理论，完整地解决了这类迁移算子本征值的分布问题，证明了∑∞ｎ＝１ｅ６Ｒｅλｎτ＜＋∞，其中｛λｎ｝∞ｎ＝１是一列迁移算子本征值，τ是粒子的最大逃逸时间，且对其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 a anisotropic,Continuate energy,nonhomogeneous Convex medium.By terms of Hilbert-Schmidt Operator theory on Hilbert space.We Characterized completely the eigenvalue distribution of the transport operator.We Show:∑∞n=1e 6Reλnτ <+∞,Where {λ n} ∞n=1 be a Series of eigenvalues of the transport operator,τ is the maximum escaping time .We also discussed the discrete extent of eigenvalues and enumeration function of eigenvalues.Moreover,We obtain the eigenfunction expansion of the transport equation′s solution.