Maximally degenerate laplacians

Annales de l'Institut Fourier

Volumn 46, Issue 2, 1996, Pages 547-587

  Zelditch, Steven ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Band invariants; Eigenvalue multiplicities; Non commutative residue fields; Toeplitz and fourier integral operators; Zoll metric

Indexed keywords

EID: 0030488039     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1524     Document Type: Article

References (24)

1. A. BESSE, Manifolds all of whose geodesics are closed, Ergeb, Math., 93, Springer-Verlag, New York, 1978.
2. G. BESSON, Sur la multiplicité de la première valeur propre des surfaces riernanniennes, Ann. Inst. Fourier, Grenoble, 30-1 (1980), 109-128.
3. M. BERGER, P. GAUDUCHON, E. MAZET, Le spectre d'une variété riemannienne, SLN 194, Springer-Verlag, New York, 1974.
4. L. BOUTET DE MONVEL, V. GUILLEMIN, The spectral theory of Toeplitz operators, Ann. Math. Studies, 99, Princeton Univ. Press, 1981.
5. J. BRÜNING, Heat equation asymptotics for singular Sturm-Liouville operators, Math. Ann., 268 (1984), 173-196.
6. Y. COLIN DE VERDIÈRE, Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques, Comment. Math. Helv., 54 (1979), 508-522.
7. Y. COLIN DE VERDIÈRE, Construction de laplaciens dont une partie finie du spectre est donnée, Ann. Scient. Éc. Norm. Sup., 20 (1987), 599-615.
8. H. DUISTERMAAT, V. GUILLEMIN, The spectrum of elliptic operators and periodic bicharacteristics, Inv. Math., 29 (1975), 39-79.
9. 2, Pacific J. Math., 154 (1992), 215-229.
10. A. GRAY, Tubes, Addison-Wesley, New York, 1990.
11. V. GUILLEMIN and A. URIBE, Circular symmetry and the trace formula, Invent. Math., 96 (1989), 385-423.
12. V. GUILLEMIN, Band asymptotics in two dimensions, Adv. Math., 42, 148-282.
13. V. GUILLEMIN, Some spectral results on rank one symmetric spaces, Adv. Math., 28 (1978), 129-137.
14. V. GUILLEMIN, Some spectral results for the Laplace operator with potential on the n-sphere, Adv. Math., 27 (1978), 273-286.
15. L. HÖRMANDER, The analysis of partial differential operators, vol. I-IV, Grundlehren 256-7, 274-5, Springer-Verlag, New York, 1983-84.
16. A. IVIC, The Riemann zeta function, Wiley-Interscience, John Wiley and Sons, New York, 1985.
17. R. JACOBY, One parameter transformation groups of the three sphere, Proc. AMS, 7 (1956), 131-142.
18. C. KASSEL, Le résidu non commutatif, Séminaire Bourbaki n° 708, Astérisque, 177-178 (1989), 199-229.
19. M. A. SHUBIN, Pseudo-differential operators and spectral theory, Springer-Verlag, 1987.
20. A. WEINSTEIN, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J., 44 (1977), 883-892.
21. A. WEINSTEIN, Fourier integral operators, quantization and the spectra of riernannian manifolds, in Géométrie Symplectique et Physique Mathématique, Colloq. Int. CNRS n° 237 (1975), 289-298.
22. H. WIDOM, The Laplace operator with potential on the 2-sphere, Adv. in Math., 31 (1979), 63-66.
23. S. T. YAU, Open problems in geometry, in Proc. Symp. Pure Math., vol. 54, part 1, AMS (1992), 1-28.
24. S. ZELDITCH, Fine structure of Zoll spectra, J. Fun. An., to appear.