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人口算子的谱性质

张连平   

  1. 山西大学数学系,太原 030006
  • 收稿日期:1900-01-01 修回日期:1900-01-01 出版日期:1999-07-15 发布日期:1999-07-15

张连平. 人口算子的谱性质[J]. 系统科学与数学, 1999, 19(3): 371-377.

Lian Ping ZHANG. SPECTRAL PROPERTIES OF POPULATION OPERATOR[J]. Journal of Systems Science and Mathematical Sciences, 1999, 19(3): 371-377.

SPECTRAL PROPERTIES OF POPULATION OPERATOR

Lian Ping ZHANG   

  1. Department of Mathematics, Shanxi University, Taiyuan 030006,P.R.China
  • Received:1900-01-01 Revised:1900-01-01 Online:1999-07-15 Published:1999-07-15
该文讨论人口算子的谱性质, 得到了人口算子本征值除可能有限个外均是代数单的, 人口算子本征值新的分布性质, 人口算子广义本征函数不构成基序列, L~2[0,r_2]上的人口算子根子空间完整等.
In this paper, the spectral properties of the population operator are studied. We obtain that (i) the algebraic multiplicity of every eigenvalue of the population operator, except for possibly a finite number of individual ones, equals one; (ii) the eigenvalues of the population operator have some new distribution properties; (iii) the generalized eigenfunctions do not constitute a basic sequence; (iv) when the population operator is confined in L~2[0,r_2], the root subspaces of the population operator are complete.
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