THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Jiahui Yu

,

Jie Liu

,

Alatancang Chen

APPROXIMATION OF BLOCK NUMERICAL RANGE FOR HAMILTONIAN OPERATOR MATRIX

ABSTRACT
The aim of this paper is to derive approximations for the block numerical range of unbounded block operator matrices that are block dominant. To illustrate our approach, we calculate the quartic numerical range of a concrete Hamiltonian operator matrix.
KEYWORDS
Hamiltonian operator matrix, block numerical range, spectrum
PAPER SUBMITTED: 2024-03-23
PAPER REVISED: 2024-06-23
PAPER ACCEPTED: 2024-06-23
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503085Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [2085 - 2093]
REFERENCES
  1. Gustafson, K., Rao, K. M., Numerical Range, Springer-Verlag, New York, USA, 1997
  2. Horn, R., Johnson, C., Topics in Matrix Analysis, Cambridge University Press, New York, USA, 1991
  3. Langer, H., Tretter, C., Spectral Decomposition of Some Nonselfadjoint Block Operator Matrices, J. Oper. Theory, 39 (1998), 2, pp. 339-359
  4. Tretter, C., Spectral Theory of Block Operators Matrices and Applications, Imperial College Press, London, UK, 2008
  5. Muhammad, A., Marletta, M., Approximation of the Quadratic Numerical Range of Block Operator Matrices, Integr. Equ. Oper. Theory, 74 (2012), Sept., pp. 151-162
  6. Tretter, C., Wagenhofer, M., The Block Numerical Range of an n×n Block Operator Matrix, SIAM J. Matrix Anal. Appl., 24 (2003), 4, pp. 1003-1017
  7. Yu, J., et al., Approximation of the Block Numerical Range of Block Operator Matrices, Filomat, 33 (2019), 12, pp. 3877-3881
  8. Salemi, A., Total Decomposotion and Block Numerical Range, Banach J. Math. Anal., 5 (2011), 1, pp. 51-55
  9. Alatancang, et al., Structure of the Spectrum of Infinite Dimensional Hamiltonian Operators, Sci. China Ser. A, 51 (2008), 5, pp. 915-924
  10. Azizov, T. Y., Dijksma A. A., On the Boundedness of Hamiltonian Operators. Proc. Amer. Math. Soc., 131 (2003), 2, pp. 563-576
  11. Azizov, T. Y., et al., An Indefinite Approach to the Reduction of a Nonnegative Hamiltonian Operator Function to a Block Diagonal Form, Funct. Anal. Appl., 35 (2001), 3, pp. 220-221
  12. Alatancang, Wu, D., Invertibility of Nonnegative Hamiltonian Operator with Unbounded Entries, J. Math. Anal. Appl., 373 (2011), 2, pp. 410-413
  13. Alatancang, Wu, D., A Review for Research in Spectral Theory of Infinite Dimensional Hamiltonian Operators (in Chinese), Journal of Inner Mongolia Normal University, 50 (2021), 1 pp. 1-6
  14. Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heideibeerg, New York, USA, 1980
  15. Jin, G., et al., On Invertible Nonnegative Hamiltonian Operator Matrices, Acta Mathematica Sinica, English Series, 30 (2014), 10, pp. 1763-1774
  16. Zhong, W., Zhong, X., Method of Separation of Variables and Hamiltonian System, Numer. Methods Partial Differential Equations, 9 (1993), 1, pp. 63-75
  17. Zhong, W., A New Systematic Method in Elasticity Theory (in Chinese), Dalian University of Technology Press, Dalian, China, 1995
  18. Jin, G., Topics in Theory of Hamiltonian Operators, Ph. D. thesis, Inner Monglia University, Hohhot, China, 2014
  19. Qiao, Y., et al., Block Basis Property for Systems of Eigenctors of a Class of 4×4 Unbounded Operator Matrices and Its Application In Elasticity (in Chinese), Chinese Annals of Mathematics, 42 (2021), 3, pp. 237-258
PDF VERSION [DOWNLOAD]
Approximation of block numerical range for Hamiltonian operator matrix

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence