Bounds on Schrödinger operators and generalized Sobolev type inequalities

Elliot H. Lieb

Séminaire Équations aux dérivées partielles (Polytechnique) (1985-1986)

  • page 1-8

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Lieb, Elliot H.. "Bounds on Schrödinger operators and generalized Sobolev type inequalities." Séminaire Équations aux dérivées partielles (Polytechnique) (1985-1986): 1-8. <http://eudml.org/doc/111899>.

@article{Lieb1985-1986,
author = {Lieb, Elliot H.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Sobolev type inequalities; estimate; negative eigenvalues; Coulomb systems; stability of atoms; magnetic fields},
language = {eng},
pages = {1-8},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Bounds on Schrödinger operators and generalized Sobolev type inequalities},
url = {http://eudml.org/doc/111899},
year = {1985-1986},
}

TY - JOUR
AU - Lieb, Elliot H.
TI - Bounds on Schrödinger operators and generalized Sobolev type inequalities
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1985-1986
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 8
LA - eng
KW - Sobolev type inequalities; estimate; negative eigenvalues; Coulomb systems; stability of atoms; magnetic fields
UR - http://eudml.org/doc/111899
ER -

References

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  1. [1] M. Aizenman and E.H. Lieb, On semiclassical bounds for eigenvalues of Schrödinger operators, Phys. Lett.66A, 427-429 (1978). MR598768
  2. [2] M. Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. Math.106, 93-100 (1977). Zbl0362.47006MR473576
  3. [3] I. Daubechies, Commun. Math. Phys.90, 511 (1983) Zbl0946.81521MR719431
  4. [4] E.H. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, A.M.S. Proc. Symp. in Pure Math. 36, 241-251 (1980). The result were announced in Bull. Ann. Math. Soc.82, 751-753 (1976). Zbl0445.58029MR573436
  5. [5] H.E. Lieb, An Lp bound for the Riesz and Bessel potentials of orthonormal functions, J. Funct. Anal.51, 159-165 (1983). Zbl0517.46025MR701053
  6. [6] E.H. Lieb, On characteristic exponents in turbulence, Commun. Math. Phys.92, 413-480 (1984). Zbl0598.76054MR736404
  7. [7] E.H. Lieb and M. Loss, Stability of Coulomb systems with magnetic fields: II. The many-electron atom and the one-electron molecule, Commun. Math. Phys.104, 271-282 (1986). Zbl0607.35082MR836004
  8. [8] E.H. Lieb and W.E. Thirring, Bounds for the kinetic energy of fermions which proves the stability of matter,Phys. Rev. Lett.35, 687-689 (1975). Errata 35, 1116 (1975). 
  9. [9] E.H. Lieb and W.E. Thirring, "Inequalities for the moments of the eigenvalues of the Schrödinger equation and their relation to Sobolev inequalities in studies in Mathematical Physics" (E. Lieb, B. Simon, A. Wightman eds.) Princeton University Press, 1976. Zbl0342.35044
  10. [10] E.H. Lieb and W.E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy, Ann. of Phys. (NY) 155, 494-512 (1984). MR753345
  11. [11] G.V. Rosenbljum, Distribution of the discrete spectrum of singular differential operators. Dokl. Aka. Nauk SSSR202, 1012-1015 (1972). (MR 45 # 4216). The details are given in Izv. Vyss. Ucebn. Zaved. Matem. 164 75-86 (1976). [English trans. Sov. Math. (Iz VUZ) 20, 63-71 (1976).] Zbl0249.35069MR295148

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