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

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 = 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.

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