Spectral asymptotics for Schrödinger operators with a degenerate potential

Françoise Truc

Séminaire de théorie spectrale et géométrie (2001-2002)

  • Volume: 20, page 17-22
  • ISSN: 1624-5458

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Truc, Françoise. "Spectral asymptotics for Schrödinger operators with a degenerate potential." Séminaire de théorie spectrale et géométrie 20 (2001-2002): 17-22. <http://eudml.org/doc/114466>.

@article{Truc2001-2002,
author = {Truc, Françoise},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {asymptotic growth of the number of eigenvalues; energy; Schrödinger operator; potential; classical; semi-classical},
language = {eng},
pages = {17-22},
publisher = {Institut Fourier},
title = {Spectral asymptotics for Schrödinger operators with a degenerate potential},
url = {http://eudml.org/doc/114466},
volume = {20},
year = {2001-2002},
}

TY - JOUR
AU - Truc, Françoise
TI - Spectral asymptotics for Schrödinger operators with a degenerate potential
JO - Séminaire de théorie spectrale et géométrie
PY - 2001-2002
PB - Institut Fourier
VL - 20
SP - 17
EP - 22
LA - eng
KW - asymptotic growth of the number of eigenvalues; energy; Schrödinger operator; potential; classical; semi-classical
UR - http://eudml.org/doc/114466
ER -

References

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  1. [1] J. AVRON, I. HERBST. B. SIMON, Duke. Math. J., 45 ( 1978), 847-883. Zbl0399.35029MR518109
  2. [2] Y. COLIN DE VERDIÈRE, L'asymptotique de Weyl pour les bouteilles magnétiques, Comm. Math. Phys., 105 (1986). 327-335. Zbl0612.35102MR849211
  3. [3] J.S. DE WET and MANDL, On the asymptotic distribution of eigenvalues, Proc. Roy. Soc. London Ser., 200 ( 1950), 572-580. Zbl0040.33702MR35369
  4. [4] B.M. LEVITAN, On the asymptotic behavior of Green's function and its expansion in eigenvalues of Schrödinger's equation, Math. USSR-Sb.41, 83 ( 1957), 439-458. Zbl0083.32602MR89353
  5. [5] A.G. KOSTJUCENKO, Asymptotic distribution of the eigenvalues of elliptic operators, Soviet Math. Dokl., 5 ( 1964), 1171-1175. Zbl0135.32007
  6. [6] A. MORAME and F. TRUC, Semi-classical eigenvalue asymptotics for a Schrödinger operator with a degenerate potential, Asympt. Anal., 22 ( 2000), 39-49. Zbl0947.35116MR1739517
  7. [7] M. REED and B. SIMON, Methods of Modern Mathematical Physics IV, Academic press, New York, 1978. Zbl0401.47001MR751959
  8. [8] D. ROBERT, Comportement asymptotique des valeurs propres d'opérateurs du type de Schrödinger à potentiel dégénéré, J. Math. Pures Appl., 61 ( 1982), 275-300. Zbl0511.35069MR690397
  9. [9] G.V. ROSENBLJUM, Asymptotics of the eigenvalues of the Schrödinger operator, Math. USSR- Sb., 22 (3 )( 1974), 349-371. Zbl0304.35070
  10. [10] B. SIMON, Non classical eigenvalue asymptotics, J. Funct. Anal., 53 ( 1983), 84-98. Zbl0529.35064
  11. [11] M.Z. SOLOMYAK, Asymptotics of the spectrum of the Schrödinger operator with non regular homogeneous potential, Math. USSR-Sb., 55(1) ( 1986), 19-37. Zbl0657.35099
  12. [12] E.C. TITCHMARSH, On the asymptotic distribution of eigenvalues, Quart J. Math. Oxford Ser. (2). 5 ( 1954), 228-240. Zbl0056.08305MR68078
  13. [13] F. TRUCSemi-classical asymptotics for magnetic bottles, Asympt. Anal., 15 ( 1997), 385-395. Zbl0902.35079MR1487718

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