Inverse spectral results on two-dimensional tori

Guillemin, V.

doi:10.1090/S0894-0347-1990-1035414-4

Inverse spectral results on two-dimensional tori

Author: V. Guillemin
Journal: J. Amer. Math. Soc. 3 (1990), 375-387
MSC: Primary 58G25; Secondary 35P99
DOI: https://doi.org/10.1090/S0894-0347-1990-1035414-4
MathSciNet review: 1035414
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[1] J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math. 29 (1975), no. 1, 39–79. MR 405514, https://doi.org/10.1007/BF01405172
[2] J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183–269. MR 388464, https://doi.org/10.1007/BF02392165
[3] Gregory Eskin, James Ralston, and Eugene Trubowitz, On isospectral periodic potentials in 𝑅ⁿ, Comm. Pure Appl. Math. 37 (1984), no. 5, 647–676. MR 752594, https://doi.org/10.1002/cpa.3160370505
[4] Gregory Eskin, James Ralston, and Eugene Trubowitz, On isospectral periodic potentials in 𝑅ⁿ, Comm. Pure Appl. Math. 37 (1984), no. 5, 647–676. MR 752594, https://doi.org/10.1002/cpa.3160370505
[5] G. Eskin, Inverse spectral problem for the Schrödinger equation with periodic vector potential, Comm. Math. Phys. 125 (1989), no. 2, 263–300. MR 1016872
[6] Victor Guillemin, Band asymptotics in two dimensions, Adv. in Math. 42 (1981), no. 3, 248–282. MR 642393, https://doi.org/10.1016/0001-8708(81)90042-6
[7] Victor Guillemin and Alejandro Uribe, Clustering theorems with twisted spectra, Math. Ann. 273 (1986), no. 3, 479–506. MR 824435, https://doi.org/10.1007/BF01450735
[8] V. Guillemin and A. Uribe, Monodromy in the quantum spherical pendulum, Comm. Math. Phys. 122 (1989), no. 4, 563–574. MR 1002831
[9] Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
[10] Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, https://doi.org/10.1007/BF02392052
[11] Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in modern analysis and applications, III, Springer, Berlin, 1970, pp. 87–208. Lecture Notes in Math., Vol. 170. MR 0294568
[12] François Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 1, Plenum Press, New York-London, 1980. Pseudodifferential operators; The University Series in Mathematics. MR 597144
[13] Alan Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J. 44 (1977), no. 4, 883–892. MR 482878