JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 55-59.doi: 10.6040/j.issn.1671-9352.0.2014.268

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Eigenvalue asymptotics of a class of the Dirac operator

HAO Ping-ping, WEI Guang-sheng   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, Shaanxi, China
  • Received:2014-06-11 Revised:2014-10-13 Online:2015-02-20 Published:2015-01-27

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Abstract: In this paper, we are concered with the asymptotics of the eigenvalues of the classical Dirac opertor with the piecewise smooth potentials, and give the asymptotics of the eigenvalues up to n-2 term.

Key words: Prü, asymptotics, Dirac operator, fer transform, eigenvalue

CLC Number: 

  • O175.3
[1] LEVITAN B M, SARGSJAN I S. Sturm-Liouville and Dirac Operators[M]. Dordrecht: Kluwer Academic Publishers, 1991: 185-212.
[2] HALD O H. Inverse eigenvalue problems for layered media[J]. Comm Pure Appl Math, 1997, 30:69-94.
[3] 朱俊逸. 常型Dirac算子的谱分解[J]. 郑州大学学报:理学版,2003,35(1):11-15. ZHU Junyi. The spectral resolution of constant Dirac operator[J]. Journal of Zhengzhou University: Natural Science, 2003, 35(1):11-15.
[4] 康海娣. 一个带有周期边界条件的一位Dirac算子的研究[D]. 郑州:郑州大学出版社,2011. KANG Haidi. The research on one-dimensional Dirac operator with periodic boundary condition[D]. Zhengzhou: Zhengzhou University Press, 2011.
[5] 曹之江. 常微分算子[M]. 上海:上海科技出版社,1986:65-85. CAO Zhijiang. Ordinary differential operator[M]. Shanghai: Shanghai Science Press, 1986: 65-85.
[6] ATHANASSOYLIS G A, PAPANICOLAOU V G. Eigenvalue asymptotics of layered media and their applications to the inverse problem[J]. Siam J Appl Math, 1997, 57:453-471.
[7] ANDERSSON L. Inverse eigenvalue problems with discontinuous coefficients[J]. Inverse Problems, 1988, 4:353-397.
[8] CARLSON R. An inverse spectral problem for Sturm-Liouville operators with discontinuous coefficients[J]. Proc Amer Math Soc, 1994, 120:475-484.
[9] COURANT R, HILBERT D. Methods of mathematical physics[M]. New York: Interscience Publishers, 1953.
[10] 孙丰珠. 随机Dirac算子的旋转数和谱[J]. 山东大学学报:自然科学版,1991,26(1):1-9. SUN Fengzhu. The rotation number for stochastic Dirac opertors and spectrum[J]. Journal of Shandong University: Natural Science, 1991, 26(1):1-9.
[11] KOBAYASHI M. An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials[J]. Comput Math Appl, 1989, 18:349-356.
[12] MCNAAB A, ANDERSSEN R S, LAPWOOD E R. Asymptotic behavior of the eigenvalues of a Sturm-Liouville system with discontinuous coefficients[J]. J Math Anal Appl, 1976, 54:741-751.
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