一般非均匀凸介质的迁移算子广义本征函数系统的完整性

The Completeness of Generalized Eigenfunction System of the Transport Operator for a Nonhomogeneous Convex Medium

该文讨论一般非均匀凸介质所确定的迁移算子的广义本征函数系统的完整性问题，利用我们探索的相对收敛方法，完整地刻划了一般非均匀凸介质中迁移问题的广义本征函数系统的完整性问题，我们证明了，对迁移半群E（t），当0∈Pσ（E（t）），迁移算子广义本征函数系统不完整，当0∈Pσ（E（t））时，仅当满足相对收敛条件时，迁移算子的广义本征函数系统完整．

The completeness of generalized eigenfunction system of the transport operatorfor a nonhomogeneous convex medium is discussed in this paper. By terms of the relativeconvergent method we recreat, we give a complete characterization for the problem of thecompleteness of generalized eigenfunction system of the transport operator. We show that ifO∈P(E(t) ), where {E(t) is transport semigroup , then generalized eigenfunction system of transport operator is not complete. if O P(E(t)) , then the generalized eigenfunction system is complete only and only if it satisfies the condition of relative convergence.