Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Submit a Manuscript
- Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 676835, 16 pages
doi:10.5402/2012/676835
Research Article
The Theory for -Hermitian Subspaces in a Product Space
Department of Mathematics, Shandong University at Weihai, Weihai, Shandong 264209, China
Received 6 January 2012; Accepted 13 February 2012
Academic Editors: S. Deng and O. Miyagaki
Copyright © 2012 Huaqing Sun and Jiangang Qi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, The Clarendon Press Oxford University Press, New York, NY, USA, 1987.
- W. N. Everitt and L. Markus, Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-Differential Operators, vol. 61, American Mathematical Society, Providence, RI, USA, 1999.
- J. Weidmann, Spectral Theory of Ordinary Differential Operators, vol. 1258 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1987.
- S. Z. Fu, “On the self-adjoint extensions of symmetric ordinary differential operators in direct sum spaces,” Journal of Differential Equations, vol. 100, no. 2, pp. 269–291, 1992. View at Publisher · View at Google Scholar
- J. Sun, “On the self-adjoint extensions of symmetric ordinary differential operators with middle deficiency indices,” Acta Mathematica Sinica, vol. 2, no. 2, pp. 152–167, 1986. View at Publisher · View at Google Scholar
- A. Wang, J. Sun, and A. Zettl, “Characterization of domains of self-adjoint ordinary differential operators,” Journal of Differential Equations, vol. 246, no. 4, pp. 1600–1622, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- M. Lesch and M. Malamud, “On the deficiency indices and self-adjointness of symmetric Hamiltonian systems,” Journal of Differential Equations, vol. 189, no. 2, pp. 556–615, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- Y. Shi and H. Sun, “Self-adjoint extensions for second-order symmetric linear difference equations,” Linear Algebra and its Applications, vol. 434, no. 4, pp. 903–930, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- R. Arens, “Operational calculus of linear relations,” Pacific Journal of Mathematics, vol. 11, pp. 9–23, 1961. View at Zentralblatt MATH
- H. Langer and B. Textorius, “On generalized resolvents and Q-functions of symmetric linear relations (subspaces) in Hilbert space,” Pacific Journal of Mathematics, vol. 72, no. 1, pp. 135–165, 1977.
- E. A. Coddington, Extension Theory of Formally Normal and Symmetric Subspaces, Memoirs of the American Mathematical Society, No. 134, American Mathematical Society, Providence, RI, USA, 1973.
- Y. Shi, “The Glazman-Krein-Naimark theory for Hermitian subspaces,” The Journal of Operator Theory. In press.
- E. A. Coddington, “Self-adjoint subspace extensions of nondensely defined symmetric operators,” Advances in Mathematics, vol. 14, pp. 309–332, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- E. A. Coddington and A. Dijksma, “Self-adjoint subspaces and eigenfunction expansions for ordinary differential subspaces,” Journal of Differential Equations, vol. 20, no. 2, pp. 473–526, 1976. View at Publisher · View at Google Scholar
- A. Dijksma and H. S. V. de Snoo, “Self-adjoint extensions of symmetric subspaces,” Pacific Journal of Mathematics, vol. 54, pp. 71–100, 1974. View at Zentralblatt MATH
- B. M. Brown, D. K. R. McCormack, W. D. Evans, and M. Plum, “On the spectrum of second-order differential operators with complex coefficients,” Proceedings of The Royal Society of London Series A, vol. 455, no. 1984, pp. 1235–1257, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- B. M. Brown and M. Marletta, “Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems,” Proceedings of The Royal Society of London Series A, vol. 457, no. 2005, pp. 117–139, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- J. Qi, Z. Zheng, and H. Sun, “Classification of Sturm-Liouville differential equations with complex coefficients and operator realizations,” Proceedings of The Royal Society of London Series A, vol. 467, no. 2131, pp. 1835–1850, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- A. R. Sims, “Secondary conditions for linear differential operators of the second order,” Journal of Mathematics and Mechanics, vol. 6, pp. 247–285, 1957. View at Zentralblatt MATH
- H. Sun and J. Qi, “On classification of second-order differential equations with complex coefficients,” Journal of Mathematical Analysis and Applications, vol. 372, no. 2, pp. 585–597, 2010. View at Publisher · View at Google Scholar
- H. Sun, J. Qi, and H. Jing, “Classification of non-self-adjoint singular Sturm-Liouville difference equations,” Applied Mathematics and Computation, vol. 217, no. 20, pp. 8020–8030, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- R. H. Wilson, “Non-self-adjoint difference operators and their spectrum,” Proceedings of The Royal Society of London Series A, vol. 461, no. 2057, pp. 1505–1531, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
- I. M. Glazman, “An analogue of the extension theory of Hermitian operators and a non-symmetric one-dimensional boundary problem on a half-axis,” Doklady Akademii Nauk SSSR, vol. 115, pp. 214–216, 1957 (Russian). View at Zentralblatt MATH
- D. Race, “The theory of J-self-adjoint extensions of J-symmetric operators,” Journal of Differential Equations, vol. 57, pp. 258–274, 1985.
- Z. J. Shang, “On J-self-adjoint extensions of J-symmetric ordinary differential operators,” Journal of Differential Equations, vol. 73, no. 1, pp. 153–177, 1988. View at Publisher · View at Google Scholar
- I. Knowles, “On the boundary conditions characterizing J-self-adjoint extensions of J-symmetric operators,” Journal of Differential Equations, vol. 40, no. 2, pp. 193–216, 1981. View at Publisher · View at Google Scholar
- J. L. Liu, “J self-adjoint extensions of J symmetric operators,” Acta Scientiarum Naturalium Universitatis Intramongolicae, vol. 23, no. 3, pp. 312–316, 1992.