Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (6): 1559-1566.

• Articles • Previous Articles     Next Articles

The Convergence or Divergence for Eigenfunction Expansion of Infinite Dimensional Hamiltonian Operator

 WU De-Yu, Alatancang   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
  • Received:2010-08-13 Revised:2011-09-06 Online:2011-12-25 Published:2011-12-25

Abstract:

In this paper, we study the eigenfunction systems of infinite dimensional Hamiltonian operator and obtain a class of infinite dimensional Hamiltonian operators whose eigenfunction systems are not complete in Hilbert space X×X, which is helpful to solve the problems that the method of separation of variable whether can be used in a class of Hamiltonian systems. In the end, concrete examples are constructed to justify the effectiveness of the criterion.

Key words: Infinite dimensional Hamiltonian operator, k-compact operator, Eigenfunction system, Cauchy principal value, Completeness

CLC Number: 

  • 35P10
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