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

Xu Genqi(Department of Mathematics, Shanxi University, Taiyun 030006)Yang Mingzhu(Institute of Atomic energy Academia Sinica, Beijing 102413)Wang Shenghua (Department of Mathematics, Shangrao teacher's college, Jiangxi 334001)  
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.
【Fund】: 山西省教委青年学科带头人专项基金
【CateGory Index】: O177
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