Semiclassical spectral estimates for toeplitz operators

Annales de l'Institut Fourier

Volumn 48, Issue 4, 1998, Pages 1189-1229

  Borthwick, D ^a   Paul, T ^b   Uribe, A ^c  

^a EMORY UNIVERSITY   (United States)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

^c UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Geometric quantization; Semi classical analysis; Spectral theory; Toeplitz operators

Indexed keywords

EID: 0032272119     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1654     Document Type: Article

References (28)

1. V. I. ARNOL'D, Une classe caractéristique intervenant dans les conditions de quantification, in V. P. MASLOV, Théorie des perturbations et Méthodes asymptotiques, Dunod, Paris (1972) 341-361.
2. F. A. BEREZIN, General concept of quantization, Comm. Math. Phys., 40 (1975), 153-174.
3. N. L. BALAZS and A. VOROS, The quantized Baker's transformation, Annals of Physics, 180 (1989), 1-31.
4. M. BORDEMANN, E. MEINRENKEN, and M. SCHLICHENMAIER, Toeplitz quantization of Kähler manifolds and gl(N), N → ∞ limits, Comm. Math. Phys., 165 (1994), 281-296.
5. D. BORTHWICK, T. PAUL, and A. URIBE, Legendrian distributions and non-vanishing of Poincaré series, Invent. Math., 122 (1995), 359-402.
6. L. BOUTET de MONVEL, On the index of Toeplitz operators of several complex variables, Invent. Math., 50 (1979), 249-272.
7. L. BOUTET de MONVEL, Hypoelliptic operators with double characteristics and related pseudodifferentiel operators, Comm. Pure Appl. Math., 27 (1974), 585-639.
8. L. BOUTET de MONVEL and V. GUILLEMIN, The spectral theory of Toeplitz operators. Annals of Mathematics Studies No. 99, Princeton University Press, Princeton, New Jersey (1981).
9. L. BOUTET de MONVEL and J. SJÖSTRAND, Sur la singularité des noyaux de Bergmann et de Szego, Astérisque, 34-35 (1976), 123-164.
10. M. CAHEN, S. GUTT, and J. RAWNSLEY, Quantization of Kähler manifolds. I: geometric interpretation of Berezin's quantization, J. Geom. Phys. 7 (1990) 45-62; Quantization of Kähler manifolds. II, Trans. Amer. Math. Soc., 337 (1993) 73-98 ; Quantization of Kähler manifolds. III, preprint (1993).
11. M. CAHEN, S. GUTT, and J. RAWNSLEY, Quantization of Kähler manifolds. I: geometric interpretation of Berezin's quantization, J. Geom. Phys. 7 (1990) 45-62; Quantization of Kähler manifolds. II, Trans. Amer. Math. Soc., 337 (1993) 73-98 ; Quantization of Kähler manifolds. III, preprint (1993).
12. M. CAHEN, S. GUTT, and J. RAWNSLEY, Quantization of Kähler manifolds. I: geometric interpretation of Berezin's quantization, J. Geom. Phys. 7 (1990) 45-62; Quantization of Kähler manifolds. II, Trans. Amer. Math. Soc., 337 (1993) 73-98 ; Quantization of Kähler manifolds. III, preprint (1993).
13. M. DEGLI ESPOSTI, S. GRAFFI and S. ISOLA, Stochastic properties of the quantum Arnol'd cat in the classical limit, Comm. Math. Phys., 167 (1995), 471-509.
14. J. DIXMIER, Enveloping Algebras, North-Holland, 1977.
15. J. J. DUISTERMAAT and V. GUILLEMIN, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math., 29 (1975), 39-79.
16. G.B. FOLLAND, Harmonic Analysis in Phase Space, Annals of Mathematics Studies 122, Princeton University Press, Princeton N.J. 1989.
17. S. GRAFFI and T. PAUL, Quantum intrinsically degenerate and classical secular perturbation theory, preprint.
18. V. GUILLEMIN, Symplectic spinors and partial differential equations. Coll. Inst. CNRS 237, Géométrie Symplectique et Physique Mathématique, 217-252.
19. V. GUILLEMIN and S. STERNBERG, Geometric quantization and multiplicities of group representations, Invent. Math., 67 (1982), 515-538.
20. V. GUILLEMIN and A. URIBE, Circular symmetry and the trace formula, Invent. Math., 96 (1989), 385-423.
21. J.H. HANNAY and M.V. BERRY, Quantization of linear maps-Fresnel diffraction by a periodic grating, Physica, D 1 (1980), 267-291.
22. L. HÖRMANDER, The analysis of linear partial differential operators I-IV, Springer-Verlag, 1983-1985.
23. T. PAUL and A. URIBE, The semi-classical trace formula and propagation of wave packets, J. Funct. Analysis, 132, No.1 (1995), 192-249.
24. T. PAUL and A. URIBE, On the pointwise behavior of semi-classical measures, Comm. Math. Phys., 175 (1996), 229-258.
25. T. PAUL and A. URIBE, Weighted Weyl estimates near an elliptic trajectory, Revista Matemática Iberoamericana, 14 (1998), 145-165.
26. D. ROBERT, Autour de l'approximation semi-classique, Birkhauser 1987.
27. M. TAYLOR and A. URIBE, Semiclassical spectra of gauge fields, J. Funct. Anal., 110 (1992), 1-46.
28. L. YAFFE, Large N limits as classical mechanics, Rev. Mod. Phys., 54 (1982), 407-435.