Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 157-170.

• Articles • Previous Articles     Next Articles

A New Description of Self-adjoint Domains of Singular Linear Hamiltonian Operators

 ZHENG Zhao-Wen, XU Yan-Li   

  1. School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
  • Received:2012-10-08 Revised:2013-09-06 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金(11171178, 11271225)和高校博士点专项科研基金(20103705110003)资助.

Abstract:

In this paper, the self-adjoint extension of the  minimal Hamiltonian operator  h with equal deficiency index (d, d) is considered. Since  Im(h* y, y) can be represented as a quadratic form with rank  being 2d, the new characterization of
the domains of self-adjoint extensions of  h is obtained by the representation matrix.

Key words: Linear Hamiltonian operator, Hermitian matrix, Self-adjoint extension, Deficiency index

CLC Number: 

  • 34B05
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