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Spectral Asymptotics for More General Operators in One Dimension

  • Johannes Sjöstrand
Chapter
Part of the Pseudo-Differential Operators book series (PDO, volume 14)

Abstract

In this chapter, we generalize the results of Chap.  3. The results and the main ideas are close, but not identical, to the ones of Hager (Ann Henri Poincaré 7(6):1035–1064, 2006). We will use some h-pseudodifferential machinery, see for instance Dimassi and Sjöstrand (Spectral Asymptotics in the Semi-classical Limit, London Mathematical Society Lecture Note Series, vol 268. Cambridge University Press, Cambridge, 1999).

References

  1. 41.
    M. Dimassi, J. Sjöstrand, Spectral Asymptotics in the Semi-Classical Limit. London Mathematical Society Lecture Note Series, vol. 268 (Cambridge University Press, Cambridge, 1999)Google Scholar
  2. 47.
    V.I. Girko, Theory of Random Determinants. Mathematics and Its Applications (Kluwer Academic Publishers, Dordrecht, 1990)CrossRefGoogle Scholar
  3. 55.
    M. Hager, Instabilité spectrale semiclassique d’opérateurs non-autoadjoints. II. Ann. Henri Poincaré 7(6), 1035–1064 (2006)MathSciNetCrossRefGoogle Scholar
  4. 56.
    M. Hager, J. Sjöstrand, Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators. Math. Ann. 342(1), 177–243 (2008). http://arxiv.org/abs/math/0601381 MathSciNetCrossRefGoogle Scholar
  5. 59.
    B. Helffer, J. Sjöstrand, Multiple wells in the semiclassical limit. I. Commun. Partial Differ. Equ. 9(4), 337–408 (1984)MathSciNetCrossRefGoogle Scholar
  6. 65.
    F. Hérau, J. Sjöstrand, C. Stolk, Semiclassical analysis for the Kramers-Fokker-Planck equation. Commun. PDE 30(5–6), 689–760 (2005)MathSciNetCrossRefGoogle Scholar
  7. 67.
    M. Hitrik, Boundary spectral behavior for semiclassical operators in dimension one. Int. Math. Res. Not. 2004(64), 3417–3438 (2004)MathSciNetCrossRefGoogle Scholar
  8. 102.
    A. Melin, J. Sjöstrand, Fourier Integral Operators with Complex-Valued Phase Functions. Fourier Integral Operators and Partial Differential Equations (Colloq. Internat., Univ. Nice, Nice, 1974), pp. 120–223. Lecture Notes in Mathematics, vol. 459 (Springer, Berlin, 1975)Google Scholar
  9. 129.
    B. Simon, Semiclassical analysis of low lying eigenvalues. I. Nondegenerate minima: asymptotic expansions. Ann. Inst. H. Poincaré Sect. A (N.S.) 38(3), 295–308 (1983), Erratum in ibid 40(2), 224 (1984)Google Scholar
  10. 155.
    M. Vogel, The precise shape of the eigenvalue intensity for a class of non-selfadjoint operators under random perturbations. Ann. Henri Poincaré 18(2), 435–517 (2017). http://arxiv.org/abs/1401.8134 MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johannes Sjöstrand
    • 1
  1. 1.Université de Bourgogne Franche-ComtéDijonFrance

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