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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

Inverse spectral results on two-dimensional tori

Author(s): V. Guillemin
Journal: J. Amer. Math. Soc. 3 (1990), 375-387.
MSC: Primary 58G25; Secondary 35P99
MathSciNet review: 1035414
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References:

[1]
J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), 39-79. MR 0405514 (53:9307)

[2]
J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), 183-269. MR 0388464 (52:9300)

[3]
G. Eskin, J. Ralston, and E. Trubowitz, On isospectral periodic potentials in $ {{\mathbf{R}}^n}$, Comm. Pure Appl. Math. 37 (1984), 647-676. MR 752594 (86e:35109a)

[4]
-, On isospectral periodic potentials in $             {{\mathbf{R}}^n}$. II, Comm. Pure Appl. Math. 37 (1984), 715-753. MR 762871 (86e:35109b)

[5]
G. Eskin, Inverse spectral problems for the Schroedinger equation with a periodic vector potential, Comm. Math. Phys. 125 (1989), 263-300. MR 1016872 (91a:35052)

[6]
V. Guillemin, Band asymptotics in two dimensions, Adv. in Math. 42 (1981), 248-282. MR 642393 (83b:58015)

[7]
V. Guillemin and A. Uribe, Clustering theorems with twisted spectra, Math. Ann. 273 (1986), 479-507. MR 824435 (87g:58121)

[8]
-, Monodromy in the quantum spherical pendulum, Comm. Math. Phys. 122 (1989), 563-574. MR 1002831 (90g:81070)

[9]
L. Hörmander, The analysis of linear partial differential operators. III and IV, Springer-Verlag, Berlin and New York, 1985. MR 781536 (87d:35002a)

[10]
-, Fourier integral operators. I, Acta Math. 127 (1971), 79-183. MR 0388463 (52:9299)

[11]
B. Kostant, Quantization and unitary representations, Lecture Notes in Math., vol. 170, Springer-Verlag, Berlin and New York, 1970, pp. 87-208. MR 0294568 (45:3638)

[12]
F. Treves, Introduction to pseudodifferential and Fourier integral operators, vols. 1 and 2, Plenum Press, New York, 1980. MR 597144 (82i:35173)

[13]
A. Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J. 44 (1977), 883-892. MR 0482878 (58:2919)

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Additional Information:

DOI: 10.1090/S0894-0347-1990-1035414-4
PII: S0894-0347-1990-1035414-4
Copyright of article: Copyright 1990, American Mathematical Society




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