Clustering for the spectrum of h-pseudodifferential operators with periodic flow on an energy surface

Journal of Functional Analysis

Volumn 145, Issue 2, 1997, Pages 296-311

  Dozias, Sandrine ^a  

^a ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031569749     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1996.3023     Document Type: Article

References (22)

1. Arnold V. I. Mathematical Methods of Classical Mechanics. G. T. M. Vol. 60:1978;Springer-Verlag, Berlin.
2. Balian R., Bloch C. Solution of the Schrödinger equation in terms of classical paths. Ann. of Phys. 85:1974;514-545.
3. Brummelhuis R., Uribe A. A semi-classical trace formula for Schrödinger operators. Comm. Math. Phys. 136:1991;567-584.
4. Chazarain J. Formule de Poisson pour les variétés riemanniennes. Invent. Math. 24:1974;65-82.
5. Chazarain J. Spectre d'un hamiltonien quantique et mécanique classique. Comm. Partial Differential Equations. 5:1980;595-644.
6. Colin de Verdière Y. Spectre du laplacien et longueurs des géodésiques périodiques I. Compositio Math. 27:1973;83-106.
7. Colin de Verdière Y. Sur les spectres des opérateurs à bicaractéristiques toutes périodiques. Comm. Math. Helvetici. 54:1979;508-522.
8. Combescure M., Robert D. Distribution of matrix elements and level spacings for classically chaotic systems. Ann. Inst. H. Poincaré 61:1994;443-483.
9. Dozias S. Opérateursh. C. R. Acad. Sci. Paris I. 318:1994;1103-1108.
10. S. Dozias, Opérateursh.
11. S. Dozias, Spectral Properties and Semiclassical Asymptotics forh, Rapport de Recherche L.M.E.N.S.
12. Duistermaat J. J., Guillemin V. The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math. 29:1975;39-79.
13. Guillemin V., Sternberg S. Geometric asymptotics, Mathematics Surveys. Am. Math. Soc. Vol. 14:1977.
14. Gutzwiller M. Periodic orbits and classical quantization conditions. J. Math. Phys. 12:1971;343-358.
15. Helffer B., Robert D. Calcul fonctionnel par la transformation de Mellin et applications. J. Funct. Anal. 53:1983;246-268.
16. Helffer B., Robert D. Puis de potentiel généralisés et asymptotique semi-classique. Ann. Inst. H. Poincaré 41:1984;291-331.
17. Hörmander L. The Analysis of Linear Partial Differential Operators IV. 1985;Springer, Berlin/New York.
18. Meinrenken E. Semiclassical principal symbols and Gutzwiller's trace formula. Rep. Math. Phys. 31:1992;279-295.
19. Robert D. Autour de l'approximation semiclassique. 1987;Birkhäuser, Basel.
20. Weinstein A. On the volume of manifolds, all of whose geodesics are closed. J. Differential Geom. 9:1974;513-517.
21. Weinstein A. Lectures on Symplectic Manifolds. 1976.
22. Weinstein A. Asymptotics of the eigenvalues clusters for the Laplacien plus a potential. Duke Math. J. 44:1977;883-892.