The inverse spectral problem for surfaces of revolution

Journal of Differential Geometry

Volumn 49, Issue 2, 1998, Pages 207-264

  Zelditch, Steve ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002243013     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214461019     Document Type: Article

References (28)

1. V. I. Arnold, Mathematical methods of classical mechanics, Springer, New York, 1977.
2. S. Bates & A. Weinstein, Lectures on the geometry of quantization, Berkeley lecture notes, 1996.
3. 3, C. R. Acad. Sci. Paris 282 (1976) 159-161.
4. A. Besse, On manifolds all of whose geodesics are closed, Ergeb. Math. Grenoble (3) 93, Springer, New York, 1978.
5. P. Bleher, Distribution of energy levels of a quantum free particle on a surface of revolution, Duke Math. J. 74 (1994) 45-93.
6. L. Boutet de Monvel & V. Guillemin, The Spectral Theory of Toeplitz Operators, Ann. of Math. Stud. 99 Princeton U. Press (1981).
7. J. Bruning & E. Heintze, Spektrale starrheit gewisser Drehflachen, Math. Ann. 269 (1984) 95-101.
8. G. Darboux, Théorie des surfaces. III, Gauthier-Villars, Paris 1894.
9. Y. Colin de Verdiere, Spectre conjoint d’operateurs pseudo-differentiels qui commutent I: Le cas non-integrable, Duke Math. J. 46 (1979) 169-182.
10. Y. Colin de Verdiere, Sur les longuers des trajectoires périodiques d’un billard, (P. Dazord and N. Desolneux-Moulis eds.), Geometrie Symplectique et de Contact: Autour du Theoreme de Poincaré-Birkhoff. Travaux en Cours, Sem. Sud-Rhodanien de Geometrie III Pairs: Herman, 1984, 122-139.
11. Y. Colin de Verdiere, Quasi-modes sur les variétés Riemanniennes, Invent. Math. 43 (1977) 15-52.
12. C. Croke & B. Kleiner, Conjugacy and rigidity for manifolds with a parallel vector field, J. Differential Geom. 39 (1994) 659-680.
13. J. J. Duistermaat, On the existence of global action-angle variables, Comm. Pure. Appl. Math. 33 (1980) 687-706.
14. J. J. Duistermaat & V. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975) 29-79.
15. J. P. Françoise & V. Guillemin, On the period spectrum of a symplectic mapping, J. Funct. Anal. 100 (1991) 317-358.
16. I. M. Gel’fand & G. E. Shilov, Generalized Functions, Vol. 1, Academic Press, New York, 1964.
17. V. Guillemin, Wave trace invariants, Duke Math. J. 83 (1996) 287-52.
18. V. Guillemin & S. Sternberg, Symplectic techniques in Physics. Cambridge Univ. Press, New York, 1985.
19. V. Guillemin & S. Sternberg, Homogeneous quantization and multiplicities of group representations, J. Funct. Anal. 47 (1982) 344-380.
20. D. Gurarie, Semiclassical eigenvalues and shape problems on surfaces of revolution, J. Math. Phys. 36 (1995) 1934-1944.
21. M. Kac, On applying mathematics: reflections and examples, Mark Kack: Probability, Number Theory, and Statistical Physics, (K.Baclawski and M.D.Donskder eds.), MIT Press, Cambridge, 1979.
22. W. Klingenberg, Lectures on Closed Geodesics, Grundlehren Math. Wiss. Vol. 230, Springer, 1978.
23. V. P. Maslov, Theorie des Perturbations et Methods Asymptotiques, Dunod, Paris, 1972.
24. G. Popov, Length spectrum invariants of Riemannian manifolds, Math. Z. 213 (1993) 311-351.
25. S. Zelditch, Wave invariants at elliptic closed geodesics, Geom. Funct. Anal. 7 (1997) 145-213.
26. S. Zelditch, Wave invariants at non-degenerate closed geodesics, Geom. Funct. Anal. 8 (1998) 179-217.
27. S. Zelditch, Isospectrality in the FLO category, J. Differential Geom. 35 (1992) 689-710.
28. S. Zelditch, Kuznecov sum formulae and Szeg'o limit formulae on manifolds, Comm. Partial Differential Equations 17 (1992) 221-260.