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Reverse Lieb-Thirring inequality for the half-line matrix Schrödinger operator

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EN
Abstrakty
EN
We prove a reverse Lieb–Thirring inequality with a sharp constant for the matrix Schrödinger equation on the half-line.
Rocznik
Strony
899--916
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
  • Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, IIMAS-UNAM, Ciudad de México, CP 01000, México
Bibliografia
  • [1] T. Aktosun, R.Weder, Direct and Inverse Scattering for the Matrix Schrödinger Equation, Springer, Switzerland, 2021.
  • [2] T. Aktosun, R. Weder, The transformations to remove or add bound states for the half-line matrix Schrödinger operator, arXiv:2402.12136 [math-ph] (2024).
  • [3] S. Bachman, R. Froese, S. Schraven, Two-sided Lieb–Thirring bounds, J. Spectr. Theory 13 (2023), 1445–1472.
  • [4] A. Ben-Israel, T.N.E. Greville, Generalized Inverses Theory and Applications, 2nd ed., Springer, New York, 2003.
  • [5] G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, AMS, Providence, RI, 2013.
  • [6] A. Boumenir, V.K. Tuan, A trace formula and Schminke inequality on the half-line, Proc. Amer. Math. Soc. 137 (2009), 1039–1049.
  • [7] S.L. Campbell, C.D. Meyer, Generalized Inverses of Linear Transformations, SIAM, Philadelphia, 2009.
  • [8] K. Chadan, P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed., Springer, New York, 1989.
  • [9] D. Damanik, C. Remling, Schrödinger operators with many bound states, Duke. Math. J. 136 (2007), 51–80.
  • [10] T. Ekholm, R.L. Frank, Lieb–Thirring inequalities on the half-line with critical exponent, J. Eur. Math. Soc. 10 (2008), 739–755
  • [11] P. Exner, A. Laptev, M. Usman, On some sharp spectral inequalities for Schrödinger operator on the semi axis, Comm. Math. Phys 326 (2014), 531–541
  • [12] R.L. Frank, A. Laptev, T. Weidl, Schrödinger Operators: Eigenvalues and Lieb–Thirring Inequalities, Cambridge University Press, Cambridge, 2023.
  • [13] I.M. Gel’fand, B.M. Levitan, On the determination of a differential equation from its spectral function, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 309–360 (in Russian) [Am. Math. Soc. Transl. (ser. 2) 1 (1951), 253–304, English translation].
  • [14] V. Glaser, H. Grosse, A. Martin, Bounds on the number of eigenvalues of the Schrödinger operator, Comm. Math. Phys. 59 (1978), 197–212.
  • [15] D. Hundertmark, E.H. Lieb, L.E. Thomas, A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator, Adv. Theor. Math. Phys. 2 (1998), 719–731.
  • [16] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin, 1976.
  • [17] P. Kurasov, Spectral Geometry of Graphs, Birkäuser–Springer, Berlin, 2024.
  • [18] L.D. Landau, E.M. Lifschitz, Quantum Mechanics, Non-relativistic Theory, 3rd ed., Pergamon Press, New York, 1989.
  • [19] B.N. Levitan, Inverse Sturm–Liouville Problems, VNU Science Press, Utrecht, 1987.
  • [20] B.M. Levitan, M.G. Gasymov, Determination of a differential operator by two of its spectra, Russian Math. Surveys 19 (1964), 1–63.
  • [21] E.H. Lieb, W.E. Thirring, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relations to Sobolev inequalities, [in:] E.H. Lieb, A.S. Whightmann, B. Simon (eds), Studies in Mathematical Physics (Essays in Honor of Valentin Bargmann), Princeton University Press, Princeton, NJ, 1976, 269–303.
  • [22] V.A. Marchenko, Sturm–Liouville Operators and Applications, Revised ed., MS Chelsea, Providence, RI, 2011.
  • [23] M. Reed, B. Simon, Methods of Modern Mathematical Physics IV: Analysis of Operators, Academic Press, New York, 1978.
  • [24] L. Schimmer, Improved spectral inequalities for Schrödinger operators on the semi-axis, J. Spectr. Theory 13 (2023), 47–62.
  • [25] U.-W. Schmincke, On Schrödinger’s factorization method for Sturm–Liouville operators, Proc. Royal Soc. Edinburgh 80 A (1978), 67–84.
  • [26] T. Weidl, On the Lieb–Thirring constant Lγ,1 for γ ≥ 1/2, Comm. Math. Phys. 178 (1996), 135–146.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-60866cf6-c706-4910-8869-25c1d2b50c7a
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