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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 3
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Original Articles

Absolutely continuous spectrum of a typical operator on a cylinder

Pages 375-395 | Received 14 Oct 2015, Accepted 27 Dec 2015, Published online: 10 Feb 2016

References

  • Denisov S. On the preservation of the absolutely continuous spectrum for Schrodinger operators. J. Funct. Anal. 2006;231:143–156.
  • Birman MSh, Solomyak MZ. Spectral theory of self-adjoint operators in a Hilbert space. Springer; 1987. Translated from Russian. Mathematics and its Applications (Soviet Series). D. Reidel Publishing Co., Dordrecht.
  • Killip R, Simon B. Sum rules for Jacobi matrices and their application to spectral theory. Ann. Math. 2003;158:253–321.
  • Safronov O. Absolutely continuous spectrum of a one-parametric family of Schrödinger operators. St. Petersburg Math. J. 2013;24:977–989.
  • Pushnitski A. Spectral shift function of the Schrodinger operator in the large coupling constant limit. Commun. PDE. 2000;25:703–736.
  • Bourgain J. On random Schrödinger operators on ℝ2. Discrete Continuous Dyn. Syst. 2002;8:1–15.
  • Bourgain J. Random lattice Schrödinger operators with decaying potential: some multidimensional phenomena. Milman VD, Schechtman G, editors. Geometric aspects of functional analysis: Israel seminar 2001–2002. Vol. 1807, Lecture notes in mathematics. Berlin: Springer; 2003. p. 70–98.
  • Denisov S. On the absolutely continuous spectrum of Dirac operator. Commun. Partial Differ. Equ. 2004;29:1403–1428.
  • Denisov S. Absolutely continuous spectrum of multidimensional Schrödinger operator. Int. Math. Res. Not. 2004;74:3963–3982.
  • Denisov S. On the preservation of absolutely continuous spectrum for Schrödinger operators. J. Funct. Anal. 2006;231:143–156.
  • Denisov S. Schrödinger operators and associated hyperbolic pencils. J. Func. Anal. 2008;254:2186–2226.
  • Denisov S. Wave Propagation through sparse potential barriers. Commun. Pure Appl. Math. 2008;61:156–185.
  • Laptev A, Naboko S, Safronov O. Absolutely continuous spectrum of Schrödinger operators with slowly decaying and oscillating potentials. Comm. Math. Phys. 2005;253:611–631.
  • Perelman G. Stability of the absolutely continuous spectrum for multidimensional Schrödinger operators. Int. Math. Res. Not. 2005;37:2289–2313.
  • Safronov O. On the absolutely continuous spectrum of multi-dimensional Schrödinger operators with slowly decaying potentials. Commun. Math. Phys. 2005;254:361–366.
  • Safronov O. Multi-dimensional Schrödinger operators with some negative spectrum. J. Funct. Anal. 2006;238:327–339.
  • Safronov O. Multi-dimensional Schrödinger operators with no negative spectrum. Ann. Henri Poincare. 2006;7:781–789.
  • Safronov O. Absolutely continuous spectrum of one random elliptic operator. J. Funct. Anal. 2008;225:755–767.
  • Safronov O. Absolutely continuous spectrum of multi-dimensional Schrödinger operators with slowly decaying potentials. special issue of AMS Translations, in honor of M.S. Birman’s 80th birthday; 2008. p. 205–214 ( Amer. Math. Soc. Transl. Ser. 2, vol. 225; Amer. Math. Soc., Providence, RI).
  • Safronov O, Stolz G. Absolutely continuous spectrum of Schrödinger operators with potentials slowly decaying inside a cone. J. Math. Anal. Appl. 2007;326:192–208.
  • Safronov O. Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential. Proc. Am. Math. Soc. 2014;142:639–649.
  • Safronov O. Lower bounds on the eigenvalues of the Schrodinger operator and the spectral conservation law. J. Math. Sci (N. Y.). 2010;166:300–318.
  • Safronov O. Absolutely continuous spectrum of the Schrödinger operator with a potential representable as a sum of three functions with special propertiesl. J. Math. Phys. 2013;54:122101.
  • Denisov S, Kiselev A. 2007. Spectral properties of the Schrödinger operators with decaying potentials. Vol. 76, Proceedings of Symposia in Pure Mathematics. Providence, RI: AMS.

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