Generalized Spectrum and Numerical Rang of Matrix the Lorentzian Oscillator Group of Dimension Four
Main Article Content
Abstract
In this paper, we find the spectrum, pseudo-spectrum and numerical rang of matrix of the metric ga.
Article Details
References
- M. Boucetta, A. Medina. Solutions of the Yang-Baxter equations on orthogonal groups: the case of oscillator groups, J. Geom. Phys. 61 (2011), 2309-2320.
- S. Bromberg, A. Medina, Geometry of oscillator groups and locally symmetric manifolds, Geom. Dedicata. 106 (2004), 97-111.
- G. Calvaruso, J. Van der Veken: Totally geodesic and parallel hypersurfaces of four-dimensional oscillator groups. Results Math. 64 (2013), 135-153.
- G. Calvaruso, A. Zaeim, On the symmetries of the Lorentzian oscillator group, Collect. Math. 68 (2017), 51-67.
- R. Duran Diaz, P.M. Gadea, J.A. OubiËœna: Reductive decompositions and Einstein-Yang-Mills equationsassociated to the oscillator group. J. Math. Phys. 40 (1999), 3490-3498.
- R. Duran Diaz, P.M. Gadea, J.A. OubiËœna: The oscillator group as a homogeneous spacetime. Lib. Math. 19 (1999), 9-18.
- P.M. Gadea, J.A. Oubina: Homogeneous Lorentzian structures on the oscillator groups. Arch. Math. 73 (1999), 311-320.
- K.E. Gustafson and D.K.M. Rao, Numerical Range, Springer, New York, 1997.
- R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
- V. Khiem Ngo, An Approach of Eigenvalue Perturbation Theory. Appl. Numer. Anal. Comput. Math. 2 (2005), 108-125.
- A. V. Levichev, Chronogeometry of an electromagnetic wave given by a biinvariant metric on the oscillator group, Siberian Math. J. 27 (1986), 237-245.
- A. Medina, Groupes de Lie munis de metriques bi-invariantes, Tohoku Math. J. 37 (1985), 405-421.
- A. Medina, P. Revoy, Les groupes oscillateurs et leurs r ´eseaux, Manuscripta Math. 52 (1985), 81-95.
- A. Medina-Perea, Groupes de Lie munis de pseudo-metriques de Riemann bi-invariantes. Seminaire de Geometrie Differentielle 1981-1982, Expose 4, Institut de Mathematiques, Universite des Sciences et Techniques du Languedoc, Montpellier
- J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. Math. 21 (1976), 283-329.
- D. Muller, F. Ricci. On the Laplace-Beltrami operator on the oscillator group. J. Reine Angew. Math. 390 (1988), 193-207.
- T. Nomura, The Paley-Wiener theorem for the oscillator group, J. Math. Kyoto Univ. 22 (1982/83), 71-96.
- B. O'Neill, Semi-Riemannian Geometry, Academic Press, New York, (1983).
- L. Reichel, L.N. Trefethen, Eigenvalues and pseudo-eigenvalues of Toeplitz Matrice, Linear Algebra Appl. 162-164 (1992), 153-185.
- R.F. Streater, The representations of the oscillator group, Commun. Math. Phys. 4 (1967), 217-236.
- L. Trefethen, M. Embree, Spectra and Pseudospectra: The Behavior of Non-Normal Matrices and Operators, Princeton University Press, Princeton, 2005.
- L.N. Trefethen, Pseudospectra of matrices, in D.F. Griffiths and G.A. Watson, eds., Numerical Analysis 1991, Longman, Harlow, UK, 1992.
- C. Van Loan, A study of the matrix exponential, Numerical Analysis Report No. 10, University of Manchester, UK, August, 1975, Reissued as MIMS EPrint, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, November 2006.