CLR-estimate revisited : Lieb's approach with non path integrals

G. Rozenblum; Michael Solomyak

Journées équations aux dérivées partielles (1997)

  • page 1-10
  • ISSN: 0752-0360

How to cite

top

Rozenblum, G., and Solomyak, Michael. "CLR-estimate revisited : Lieb's approach with non path integrals." Journées équations aux dérivées partielles (1997): 1-10. <http://eudml.org/doc/93340>.

@article{Rozenblum1997,
author = {Rozenblum, G., Solomyak, Michael},
journal = {Journées équations aux dérivées partielles},
keywords = {negative eigenvalues; Schrödinger operator; Cwikel-Lieb-Rozenblum estimation},
language = {eng},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {CLR-estimate revisited : Lieb's approach with non path integrals},
url = {http://eudml.org/doc/93340},
year = {1997},
}

TY - JOUR
AU - Rozenblum, G.
AU - Solomyak, Michael
TI - CLR-estimate revisited : Lieb's approach with non path integrals
JO - Journées équations aux dérivées partielles
PY - 1997
PB - Ecole polytechnique
SP - 1
EP - 10
LA - eng
KW - negative eigenvalues; Schrödinger operator; Cwikel-Lieb-Rozenblum estimation
UR - http://eudml.org/doc/93340
ER -

References

top
  1. AHSim. Y. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J. 45 (1978), 847-883. Zbl0399.35029
  2. Ca. R. Carmona, Path integrals for relativistic Schrödinger operators, Proc. Nordic Summer School in Math., Lecture Notes Physics 345 (1989), 66-92. Zbl0712.35069MR91g:60088
  3. Co. J. Conlon, A new proof of the Cwickel-Lieb-Rozenbljum bound, Rocky Mountain J. Math. 15 (1985), 117-122. Zbl0581.35014MR86j:35118
  4. Cw. M. Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. Math. 106 (1977), 93-100. Zbl0362.47006MR57 #13242
  5. D. I. Daubechies, An uncertainity principle for fermions with generalized kinetic energy, Commun. Math. Phys. 90 (1983), 511-520. Zbl0946.81521MR85j:81008
  6. LevS. D. Levin and M. Solomyak, Rozenblum-Lieb-Cwikel inequality for Markov generators, Jour. d'Anal. Math 71 (1997), 173-193. Zbl0910.47017MR98j:47090
  7. LiY. P. Li and S-T. Yau, On the Schrödinger equation and the eigenvalue problem, Comm. Math. Phys. 88 (1983), 309-318. Zbl0554.35029MR84k:58225
  8. L1. E.H. Lieb, Bounds on the eigenvalues of the Laplace and Schrödinger operators., Bull. of the AMS 82 (1976), 751-753. Zbl0329.35018MR53 #11679
  9. L2. E.H. Lieb, Kinetic energy bounds and their application to the stability of matter, Proc. Nordic Summer School in Math. Lecture Notes Physics 354 (1989), 371-382. Zbl0698.35134MR91a:82045
  10. MRoz. M. Melgaard and G. Rozenblum, Spectral estimates for magnetic operators, Mathematica Scandinavica (to appear). Zbl0888.35074
  11. RSim. M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol. 4, Academic Press, New York, San Francisco, London, 1978. Zbl0401.47001
  12. Roz. G.V. Rozenblum (Rozenbljum), The distribution of the discrete spectrum for singular differential operators, Dokl. Akad. Nauk SSSR 202 (1972), 1012-1015 (Russian) ; English transl. in Soviet Math. Dokl 13 (1972). Zbl0249.35069
  13. RozS. G.V. Rozenblum and M. Solomyak, CLR-estimate for the generators of positivity preserving and positively dominated semigroups, prepint ESI 447 (1997). Zbl0911.47025
  14. Sh. M. Shubin, Discrete magnetic Laplacian, Commun. Math. Phys. 164 (1994), 157-172. Zbl0811.46079MR97b:82010
  15. Sim. B. Simon, Functional Integration and Quantum Physics, Academic Press, NY, 1979. Zbl0434.28013MR84m:81066

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.