Numerical Range of Left Invariant Lorentzian Metrics on the Heisenberg Group H₃ of Dimension Three

Year 2021, Volume: 18 Issue: 2, 81 - 86, 01.11.2021

Derkaoui Rafik , Abderrahmane Smaıl

Abstract

The study of eigenvalues and numerical range appears in diffrent scientific fields. We can cite for example the domain of physics, spectral theory, the stability of dynamics electricity, the quantum mechanics. In this paper, we find the spectrum, pseudospectrum and numerical range of left invariant Lorentzian metrics on the Heisenberg group H3 of dimension three. An example is given for metrics g1 and g2 while the second example is provided to support g3.

Keywords

Heisenberg group, Lorentz metric, Bounded operator, Spectrum, Pseudo-spectrum, Numerical range

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