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Structure of the spectrum of infinite dimensional Hamiltonian operators

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Abstract

This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators. It is shown that the spectrum, the union of the point spectrum and residual spectrum, and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover, it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis; and a complete characterization of the residual spectrum in terms of the point spectrum is then given. As applications of these structure results, we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences and Technology, Inner Mongolia University, Hohhot, 010021, China

    Alatancang, JunJie Huang & XiaoYing Fan

Authors
  1. Alatancang
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  2. JunJie Huang
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  3. XiaoYing Fan
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Corresponding author

Correspondence to JunJie Huang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10562002) and the Natural Science Foundation of Inner Mongolia (Grant Nos. 200508010103, 200711020106)

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Alatancang, Huang, J. & Fan, X. Structure of the spectrum of infinite dimensional Hamiltonian operators. Sci. China Ser. A-Math. 51, 915–924 (2008). https://doi.org/10.1007/s11425-007-0187-0

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  • DOI: https://doi.org/10.1007/s11425-007-0187-0

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