Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Strong limit-point classification of singular Hamiltonian expressions


Authors: Jiangang Qi and Shaozhu Chen
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1667-1674
MSC (2000): Primary 34B20; Secondary 47B25
DOI: https://doi.org/10.1090/S0002-9939-04-07037-6
Published electronically: January 7, 2004
MathSciNet review: 2051127
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Strong limit-point criteria for singular Hamiltonian differential expressions with complex coefficients are obtained. The main results are extensions of the previous results due to Everitt, Giertz, and Weidmann for scalar differential expressions.


References [Enhancements On Off] (What's this?)

  • 1. F. V. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York, 1964. MR 31:416
  • 2. S. L. Clark, A criterion for absolute continuity of the continuous spectrum of a Hamilton system, J. Math. Anal. Appl. 151 (1990), 108-128. MR 91i:34097
  • 3. N. Dunford and J. T. Schwartz, Linear operators, Part II, Spectral theory: Self-adjoint operators in Hilbert space, Interscience, New York, 1963. MR 32:6181
  • 4. W. N. Everitt, On the limit-point classification of second-order differential operators, J. London Math. Soc. 41 (1966), 531-534. MR 34:410
  • 5. W. N. Everitt and M. Giertz, On some properties of the domains of powers of certain differential operators, Proc. London Math. Soc. (3) 24 (1972), 756-768. MR 46:2492
  • 6. W. N. Everitt, M. Giertz and J. B. McLeod, On the strong and weak limit-point classification of second-order differential expressions, Proc. London Math. Soc. (3) 29 (1974), 142-158. MR 50:13701
  • 7. W. N. Everitt, M. Giertz, and J. Weidmann, Some remarks on a separation and limit-point criterion of second-order, ordinary differential expressions, Math. Ann. 200 (1973), 335-346. MR 48:4393
  • 8. W. N. Everitt, D. B. Hinton, and J. S. W. Wong, On the strong limit-$n$ classification of linear ordinary differential expressions of order $2n$, Proc. London Math. Soc. (3) 29 (1974), 351-367. MR 53:13708
  • 9. E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, London, 1969. MR 40:2939
  • 10. D. B. Hinton and J. K. Shaw, On boundary value problems for Hamiltonian systems with two singular points, SIAM. J. Math. Anal. 15 (1984), 272-286. MR 87a:34021
  • 11. D. B. Hinton and J. K. Shaw, Absolutely continuous spectra of Dirac systems with long range, short range and oscillating potentials, Quart. J. Math. Oxford Ser. (2) 36 (1985), 183-213. MR 87f:34024
  • 12. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985. MR 87e:15001
  • 13. R. M. Kauffman, T. T. Read, and A. Zettl, The deficiency index problem for powers of ordinary differential expressions, Lecture Notes in Math., vol. 621, Springer-Verlag, Berlin, 1977. MR 58:1370
  • 14. A. M. Krall, $M(\lambda )$ theory for singular Hamiltonian systems with one singular point, SIAM J. Math. Anal. 20 (1989), 664-700. MR 91c:34036
  • 15. A. M. Krall, A limit-point criterion for linear Hamiltonian systems, Applicable Analysis 61 (1996), 115-119. MR 99a:34066
  • 16. V. K. Kumar, On the strong limit-point classification of fourth-order differential expressions with complex coefficients, J. London Math. Soc. (2) 12 (1976), 287-298.
  • 17. P. W. Walker, A vector-matrix formulation for formally symmetric ordinary differential equations with applications to solutions of integrable square, J. London Math. Soc. (2) 9 (1974/75), 151-159. MR 51:6021

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34B20, 47B25

Retrieve articles in all journals with MSC (2000): 34B20, 47B25


Additional Information

Jiangang Qi
Affiliation: Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People’s Republic of China
Email: qwljg01@sohu.com

Shaozhu Chen
Affiliation: Department of Mathematics, Shandong University, Jinan, Shandong 250100, People’s Republic of China
Email: szchen@sdu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-04-07037-6
Keywords: Hamiltonian system, deficiency index, strong limit-point case
Received by editor(s): January 30, 2002
Received by editor(s) in revised form: September 6, 2002, and September 15, 2002
Published electronically: January 7, 2004
Additional Notes: This project was supported by the NSF of China under Grant 10071043
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society