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

数学物理学报 ›› 1997, Vol. 17 ›› Issue (2): 163-169.

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

许跟起¹, 阳名珠², 王胜华³

1 山西大学数学系太原 030006;
2 中国原子能科学研究院北京 102413;
3 江西上饶师范专科学校教学系上饶 334001

收稿日期:1995-04-12 修回日期:1995-11-02 出版日期:1997-04-26 发布日期:1997-04-26
基金资助:
山西省教委青年学科带头人专项基金

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

Xu Genqi¹, Yang Mingzhu², Wang Shenghua³

1 Department of Mathematics, Shanxi University, Taiyun 030006;
2 Institute of Atomic energy Academia Sinica, Beijing 102413;
3 Department of Mathematics, Shangrao teacher's college, Jiangxi 334001

Received:1995-04-12 Revised:1995-11-02 Online:1997-04-26 Published:1997-04-26

摘要/Abstract

摘要： 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∈P_σ(E(t)),迁移算子广义本征函数系统不完整,当0∈P_σ(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.

关键词: 迁移算子, 广义本征函数, 完整性

Abstract: The completeness of generalized eigenfunction system of the transport operator for a nonhomogeneous convex medium is discussed in this paper. By terms of the relative convergent method we recreat, we give a complete characterization for the problem of the completeness of generalized eigenfunction system of the transport operator. We show that if 0∈P_σ(E(t)), where {E(t) ≥ 0 is transport semigroup, then generalized eigenfunction system of transport operator is not complete. if O∉P_σ(E(t)), then the generalized eigenfunction system is complete only and only if it satisfies the condition of relative convergence.

Key words: transport operator, generalized eigenfunction system, completeness

许跟起, 阳名珠, 王胜华. 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[J]. 数学物理学报, 1997, 17(2): 163-169.

Xu Genqi, Yang Mingzhu, Wang Shenghua. The Completeness of Generalized Eigenfunction System of the Transport Operator for a Nonhomogeneous Convex Medium[J]. Acta mathematica scientia,Series A, 1997, 17(2): 163-169.

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