Pseudo-spectrum and the Numerical Range for Ricci Tensor on the Oscillator Group of Dimension Four

Authors : Bendehiba MENAD, Derkaoui RAFİK

Pages : 9-21

View : 18 | Download : 13

Publication Date : 2023-05-01

Article Type : Research Paper

Abstract :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 = Rinsert ignore into journalissuearticles values(∂i, ∂ j);, also for Ricci tensor ρ on the oscillator group insert ignore into journalissuearticles values(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