The magnetic Schrödinger operator and reverse Hölder class

Zhongwei Shen

Journées équations aux dérivées partielles (1996)

  • Volume: 1996, page 1-10
  • ISSN: 0752-0360

How to cite

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Shen, Zhongwei. "The magnetic Schrödinger operator and reverse Hölder class." Journées équations aux dérivées partielles 1996 (1996): 1-10. <http://eudml.org/doc/93324>.

@article{Shen1996,
author = {Shen, Zhongwei},
journal = {Journées équations aux dérivées partielles},
keywords = {eigenvalue asymptotics for magnetic Schrödinger operators; electric potential; magnetic field},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {The magnetic Schrödinger operator and reverse Hölder class},
url = {http://eudml.org/doc/93324},
volume = {1996},
year = {1996},
}

TY - JOUR
AU - Shen, Zhongwei
TI - The magnetic Schrödinger operator and reverse Hölder class
JO - Journées équations aux dérivées partielles
PY - 1996
PB - Ecole polytechnique
VL - 1996
SP - 1
EP - 10
LA - eng
KW - eigenvalue asymptotics for magnetic Schrödinger operators; electric potential; magnetic field
UR - http://eudml.org/doc/93324
ER -

References

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  1. [AHS] J. Avron, I. Herbst and B. Simon, Schrödinger Operators with Magnetic Fields. I. General Interaction, Duke Math. J. 45 (4) (1978), 847-883. Zbl0399.35029MR80k:35054
  2. [F] C. Fefferman, The Uncertainty Principle, Bull. Amer. Math. Soc. 9 (1983), 129-206. Zbl0526.35080MR85f:35001
  3. [Gu] D. Guibourg, Inégalités Maximales pour L'Opérateur de Schrödinger, Ph. D. Thesis, Université de Rennes-I (1992.). Zbl0783.35013
  4. [Gur] D. Gurarie, Nonclassical Eigenvalue Asymptotics for Operators of Schrödinger Type, Bull. Amer. Math. Soc. 15(2) (1986), 233-237. Zbl0628.35076MR88a:35177
  5. [H] B. Helffer, Semi-Classical Analysis for the Schrödinger Operator and Applications, Lectures Notes in Math., vol. 1336, Springer-Verlag, 1988. Zbl0647.35002MR90c:81043
  6. [HM] B. Helffer and A. Mohamed, Caractérisation du spectre essentiel de lópérateur de Schrödinger avec un champ magnétique, Ann. Inst. Fourier 38 (1988), 95-112. Zbl0638.47047MR90d:35215
  7. [HN1] B. Helffer and J. Nourrigat, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progress in Math. 58, Birkhäuser, Boston (1985). Zbl0568.35003MR88i:35029
  8. [HN2] B. Helffer and J. Nourrigat, Decrossance a l'infini des fonctions propres de l'opérateur de Schrödinger avec champ electromagnétique polynomial, J. Anal. Math. 58 (1992), 263-275. Zbl0814.35080MR95e:35049
  9. [I] A. Iwatsuka, Magnetic Schrödinger Operators with Compact Resolvent, J. Math. Kyoto Univ. 26-3 (1986), 357-374. Zbl0637.35026MR87j:35287
  10. [KS] R. Kerman and E. Sawyer, The Trace Inequality and Eigenvalue Estimates for Schrödinger Operators, Ann. Inst. Fourier (Grenoble) 36(4) (1986), 207-228. Zbl0591.47037MR88b:35150
  11. [MN] A. Mohamed and J. Nourrigat, Encadrement du N(λ) pour un opérator de Schrödinger avec un champ magnétique et un potentiel électrique, J. Math. Pures Appl. 70 (1991), 87-99. Zbl0725.35068MR92a:35122
  12. [R] D. Robert, Comportement asymptotique des valurs propres d'opérateurs du type Schrödinger á potentiel “dégénéré”, J. Math. Pures Appl. 61(9) (1982), 275-300. Zbl0511.35069MR84d:35117
  13. [Sh1] Z. Shen, Lp Estimates for Schrödinger Operators with Certain Potentials, Ann. Inst. Fourier (Grenoble) 45(2) (1995), 513-546. Zbl0818.35021MR96h:35037
  14. [Sh2] Z. Shen, On the Eigenvalue Asymptotics of Schrödinger Operators, preprint (1995). 
  15. [Sh3] Z. Shen, Eigenvalue Asymptotics and Exponential Decay of Eigenfunctions for Schrödinger Operators with Magnetic Fields, Trans. Amer. Math. Soc. (to appear). Zbl0866.35088
  16. [Sh4] Z. Shen, Estimates in Lp for Magnetic Schrödinger Operators, preprint (1995). 
  17. [Sh5] Z. Shen, On the Number of Negative Eigenvalues for a Schrödinger Operator with Magnetic Field, Comm. Math. Phys. (to appear). Zbl0863.35071
  18. [Si] B. Simon, Nonclassical Eigenvalue Asymptotics, J. Funct. Anal. 53 (1983), 84-98. Zbl0529.35064MR85i:35113
  19. [So] M. Solomjak, Spectral Asymptotics of Schrödinger Operators with Non-regular Homogeneous Potential, Math. USSR Sb. 55 (1986), 19-38. 
  20. [St] E. Stein, Harmonic Analysis : Real-Variable Method, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993. Zbl0821.42001MR95c:42002
  21. [Z] J. Zhong, Harmonic Analysis for Some Schrödinger Type Operators, Ph. D. Thesis, Princeton University, 1993. 

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