Pseudo-spectrum and Numerical Range of Matrices Walker of Dimension Three

Year 2023, Volume: 20 Issue: 1, 1 - 8, 01.05.2023

Khalef Bouich Derkaoui Rafik Abderrahmane Smaıl

Abstract

The study of numerical range, spectrum and pseudo spectrum appears in diffrent sci- entific fields, for example the domain of spectral theory, the stability of dynamics elec- tricity, physics, the quantum mechanics. In this paper, we find the spectrum, pseudo- spectrum and numerical range on Walker manifolds of dimension three. Two examples are given for metric g f .

Keywords

Bounded operator, Spectrum, Pseudo-spectrum, Numerical range, Matrix Walker.

Supporting Institution

University of oran 1 Ahmed Ben Bella, Algeria

Project Number

2

Thanks

We thank all the members of this wonderful journal with high scientific and purposeful content

References

• O. Toeplitz, ”Das algebraische Analogon zu einem Staze von Feje´r,” Math. Z., vol. 2, pp. 187-197, 1918.
• F. Hausdorff, ”Der Wertvorrat einer Bilinearform,” Math. Z., vol. 3, pp. 314-316, 1919.
• A. Wintner, ”Zur Theorie der beschra¨nkten Bilinearformen,” Math. Z., vol. 30, pp. 228-282, 1929.
• M. H. Stone, ”Linear transformations in Hilbert space and their applications to analysis,” A.M.S., New York, 1932.
• L. Reichel, L. N .Trefethen, Eigenvalues and pseudo-eigenvalues of Toeplitz Matrice, Lin. Alg. Applics. 162-164 (1992), pp. 153-185.
• M.M. Khorami, F. Ershad and B. Yousefi, ”On the Numerical Range of some Bounded Operators.” Journal of Mathe- matical Extension, vol. 15, 2020.
• M. Chaichi, E. Garc´ıa-R´ıo and M.E. Va´zquez-Abal, ”Three-dimensional Lorentz manifolds admitting a parallel null vector field,” J. Phys. A: Math. Gen., vol. 38, pp. 841-850, 2005.
• L. Trefethen and M. Embree, ”Spectra and Pseudospectra: The Behavior of Non-Normal Matrices and Operators,” Princeton University Press, Princeton, 2005.
• K. E. Gustafson and K. M. R. Duggirala, ”Numerical Range, The Field of Values of Linear Operators and Matrices,” Springer, New York, 1997.