Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques

B. Helffer; D. Robert

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1982)

  • Volume: 9, Issue: 3, page 405-431
  • ISSN: 0391-173X

How to cite

top

Helffer, B., and Robert, D.. "Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 9.3 (1982): 405-431. <http://eudml.org/doc/83886>.

@article{Helffer1982,
author = {Helffer, B., Robert, D.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {semiclassic behavior; hypo-elliptic Hamiltonian; Schrödinger operator; Weyl calculus; Fourier integral operators},
language = {fre},
number = {3},
pages = {405-431},
publisher = {Scuola normale superiore},
title = {Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques},
url = {http://eudml.org/doc/83886},
volume = {9},
year = {1982},
}

TY - JOUR
AU - Helffer, B.
AU - Robert, D.
TI - Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1982
PB - Scuola normale superiore
VL - 9
IS - 3
SP - 405
EP - 431
LA - fre
KW - semiclassic behavior; hypo-elliptic Hamiltonian; Schrödinger operator; Weyl calculus; Fourier integral operators
UR - http://eudml.org/doc/83886
ER -

References

top
  1. [1] K Asada - D. Fujiwara, On some oscillatory integral transformation in L2(Rn), Japan J. Math., 4 (1978), pp. 299-361. Zbl0402.44008MR528863
  2. [2] R. Beals, A general calculus of pseudodifferential operators, Duke Math. J,. 42 (1975), pp. 1-42. Zbl0343.35078MR367730
  3. [3] J. Chazarain, Spectre d'un hamiltonien quantique et mécanique classique, Comm. Partial Diff. Equat., 5, no. 6 (1980), pp. 595-644. Zbl0437.70014MR578047
  4. [4] B. Helffer - D. Robert, Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques, Annales de l'Institut Fourier, 31, fasc. 3 (1981), pp. 169-223. Zbl0451.35022MR638623
  5. [5] B. Helffer - D. Robert, Comportement asymptotique précisé du spectre d'opérateurs globalement elliptiques dans Rn, C. R. Acad. Sci. Paris, 292, 9 Février 1981, p. 363. Zbl0467.35074MR609080
  6. [6] B. Helffer - D. Robert, Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques, C. R. Acad. Sci. Paris, 292 (1981), p. 47. Zbl0465.35025MR610145
  7. [7] L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math., 32 (1979), pp. 359-443. Zbl0388.47032MR517939
  8. [8] L. Hörmander, On the asymptotic distribution of eigenvalues of pseudo-differential operators in Rn, Ark. för Math., 17, no. 2 (1979), pp. 296-313. Zbl0436.35064MR608322
  9. [9] Pham The Lai - D. Robert, Valeurs propres d'une classe d'équations différentielles singulières sur une demi-droite, Ann. Scuola Norm. Sup. Pisa, Série IV, 6, no. 2 (1979), pp. 335-366. Zbl0422.35062MR541452
  10. [10] D. Robert, Propriétès spectrales d'opèrateurs pseudodifférentiels, Comm. Partial Diff. E quat., 3 (1978), pp. 755-826. Zbl0392.35056MR504628
  11. [11] M.A. Subin, Pseudo-differential operators and spectral theory, Nauka, Moskva (1978). Zbl0451.47064
  12. [12] A. Voros, An algebra of pseudodifferential operators and the asymptotics of quantum mechanics, J. Functional Analysis, 29, no. 1 (1978), pp. 104-132. Zbl0386.47031MR496088

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.