PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
Rocznik
Strony
241--270
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Center of Mathematical Research of Rabat Department of Mathematics Mohammed V University of Rabat P.O. Box 1014, Marocco
  • Laboratoire de Mathematiques Pures et Appliquees Joseph Liouville EA 2597 Universite du Littoral Cote d'Opale F-62228 Calais, France
  • Center of Mathematical Research of Rabat Department of Mathematics Mohammed V University of Rabat P.O. Box 1014, Marocco
  • Laboratoire de Mathematiques Pures et Appliquees Joseph Liouville EA 2597 Universite du Littoral Cote d'Opale F-62228 Calais, France
Bibliografia
  • [1] A. Boutet de Monvel, L. Zielinski, Explicit error estimates for eigenvalues of some unbounded Jacobi matrices, Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations: IWOTA10, Oper. Theory Adv. Appl., vol. 221, Birkhauser Verlag, Basel, 2012, pp. 187-215.
  • [2] A. Boutet de Monvel, L. Zielinski, Asymptotic behaviour of large eigenvalues of a modified Jaynes-Gummings model, [in:] E. Khruslov, L. Pastur, D. Shepelsky (eds), Spectral Theory and Differential Equations, Amer. Math. Soc. Transl. Ser. 2, vol. 233, Providence, RI, 2014, pp. 77-93.
  • [3] A. Boutet de Monvel, L. Zielinski, Asymptotic behaviour of large eigenvalues for Jaynes-Gummings type models, J. Spectr. Theory 7 (2017), 1-73.
  • [4] A. Boutet de Monvel, L. Zielinski, Oscillatory behavior of large eigenvalues in quantum Rabi models, International Mathematics Research Notices, doi.org/10.1093/imrn/rny294, (2019), see also arXiv:1711.03366.
  • [5] A. Boutet de Monvel, L. Zielinski, On the spectrum of the quantum Rabi Models, Operator Theory: Advances and Applications, Birkhauser, to appear.
  • [6] A. Boutet de Monvel, J. Janas, L. Zielinski, Asymptotics of large eigenvalues for a class of band matrices, Reviews in Mathematical Physics 25 (2013) 8, 1350013.
  • [7] A. Boutet de Monvel, S. Naboko, L.O. Silva, The asymptotic behaviour of eigenvalues of a modified Jaynes-Gummings model, Asymptot. Anal. 47 (2006) 3-4, 291-315.
  • [8] P. A. Cojuhari, J. Janas, Discreteness of the spectrum for some unbounded Jacobi matrices, Acta Sci. Math. (Szeged) 73 (2007) 3-4, 649-667.
  • [9] P. Djakov, B. Mityagin, Simple and double eigenvalues of the Hill operator with a two term potential, J. Approximation Theory 135 (2005) 1, 70-104.
  • [10] P. Djakov, B. Mityagin, Trace formula and spectral Riemann surfaces for a class of tri-diagonal matrices, J. Approximation Theory 139 (2006), 293-326.
  • [11] J. Edward, Spectra of Jacobi matrices, differential equations on the circle, and the su(l, 1) Lie algebra, SIAM J. Math. Anal. 24 (2006) 3, 824-831.
  • [12] W.G. Faris, R.B. Lavine, Commutators and self-adjointness of Hamiltonian operators, Commun. Math. Phys. 35 (1974), 39-48.
  • [13] J. Janas, M. Malejki, Alternative approaches to asymptotic behaviour of eigenvalues of some unbounded Jacobi matrices, Comput. Appl. Math. 200 (2007), 342-356.
  • [14] J. Janas, S. Naboko, Infinite Jacobi matrices with unbounded entries: asymptotics of eigenvalues and the transformation operator approach, SIAM J. Math. Anal. 36 (2004) 2, 643-658.
  • [15] M. Malejki, Asymptotics of large eigenvalues for some discrete unbounded Jacobi matrices, Linear Algebra Appl. 431 (2009) 10, 1952-1970.
  • [16] M. Malejki, Asymptotics of the discrete spectrum for complex Jacobi matrices, Opuscula Math. 34 (2014) 1, 139-160.
  • [17] D. Masson, J. Repka, Spectral theory of Jacobi matrices in I (Z) the su(l,l) Lie algebra, SIAM J. Math. Anal. 22 (1991), 1131-1146.
  • [18] G.V. Rozenbljum, Near-similarity of operators and the spectral asymptotic behaviour of pseudodifjerential operators on the circle, Trudy Maskov. Mat. Obshch 36 (1978), 59-84 [in Russian].
  • [19] G. Teschl, Jacobi Operators and Completely Integrable Nonlinear Lattices, Mathematical Surveys and Monographs, vol. 72, American Mathematical Society, Providence, RI, 2000.
  • [20] E.A. Tur, Jaynes-Cummings model: solution without rotating wave approximation, Optics and Spectroscopy 89 (2000) 4, 574-588.
  • [21] E.A. Tur, Jaynes-Cummings model without rotating wave approximation, arXiv:math-ph/0211055vl (2002).
  • [22] E.A. Yanovich, Asymptotics of eigenvalues of an energy operator in a problem of quantum physics, [in:] J. Janas, P. Kurasov, A. Laptev, S. Naboko (eds), Operator Methods in Mathematical Physics OTAMP 2010, Bedlewo, Oper. Theory Adv. Appl. 227 (2013), 165-177.
  • [23] H. Volkmer, Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigen-functions of the Mathieu and spheroidal wave equation, Constr. Approx. 20 (2004) 1, 39-54.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7ec0fb63-d7bd-42cf-90c7-6eade97ff5e1
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.