Pseudo-spectrum and the Numerical Range for Ricci Tensor on the Oscillator Group of Dimension Four
Pseudo-spectrum and the Numerical Range for Ricci Tensor on the Oscillator Group of Dimension Four
The field of functional analysis presents a very interesting part of pure mathematics, but also applied mathematics such as the theory of approximations and the resolution of operational equations, the spectra of operators, pseudo-spectrum and their numerical range which are essential techniques for researchers in several fields of science and technology. In this work, we will give the notions of the numerical range of a matrix and some properties, and study it for curvature tensor Ri j = R(∂i, ∂ j), also for Ricci tensor ρ on the oscillator group (G, ga) of dimension four and we will give examples of each matrix with the use of Matlab.
Keywords:
Oscillator group, Curvature tensor, Ricci tensor, Spectrum Pseudo-spectrum, Numerical range.,
___
- 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.
- R. Derkaoui and A. Smail, ”Generalized Spectrum and Numerical Range of Matrix the Lorentzian Oscillator Group of Dimension Four,” Int. J. Anal. Appl., vol. 18, no. 6, pp. 1048-1055, 2020.
- L. Reichel and L.N. Trefethen, ”Eigenvalues and pseudo-eigenvalues of Toeplitz matrices,” Linear algebra and its applications, vol. 162, pp. 153-185, 1992.
- 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.
- G. Calvaruso and A. Zaeim, ”On the symmetries of the Lorentzian oscillator group,” Collect. Math., vol. 68, no. 51, 2017.
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2009
- Yayıncı: Çankaya Üniversitesi
Sayıdaki Diğer Makaleler
Sefiu ONİTİLO, Muhammad USMAN, Deborah DANIEL, Tola ODULE, Ajoke SANUSİ
Convergent Result for Linear Conformable Pseudo-parabolic Equation
Tuan NGUYEN ANH, Ngo HUNG, Hoang Luc NGUYEN
Mutairu KOLAWOLE, Tawakalt A. BOSEDE, Adedapo ALAJE, Kehinde A. BASHİRU, Kehinde Adekunle BASHİRU
Pseudo-spectrum and the Numerical Range for Ricci Tensor on the Oscillator Group of Dimension Four
Bendehiba MENAD, Derkaoui RAFİK
Pseudo-spectrum and Numerical Range of Matrices Walker of Dimension Three
Khalef BOUİCH, Derkaoui RAFİK, Abderrahmane SMAIL
A Generalized Series Solution of ??? Order Ordinary Differential Equations