Inverse spectral results on two-dimensional tori
HTML articles powered by AMS MathViewer
- by V. Guillemin
- J. Amer. Math. Soc. 3 (1990), 375-387
- DOI: https://doi.org/10.1090/S0894-0347-1990-1035414-4
- PDF | Request permission
References
- 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, DOI 10.1007/BF01405172
- J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183–269. MR 388464, DOI 10.1007/BF02392165
- Gregory Eskin, James Ralston, and Eugene Trubowitz, On isospectral periodic potentials in $\textbf {R}^{n}$, Comm. Pure Appl. Math. 37 (1984), no. 5, 647–676. MR 752594, DOI 10.1002/cpa.3160370505
- Gregory Eskin, James Ralston, and Eugene Trubowitz, On isospectral periodic potentials in $\textbf {R}^{n}$, Comm. Pure Appl. Math. 37 (1984), no. 5, 647–676. MR 752594, DOI 10.1002/cpa.3160370505
- G. Eskin, Inverse spectral problem for the Schrödinger equation with periodic vector potential, Comm. Math. Phys. 125 (1989), no. 2, 263–300. MR 1016872
- Victor Guillemin, Band asymptotics in two dimensions, Adv. in Math. 42 (1981), no. 3, 248–282. MR 642393, DOI 10.1016/0001-8708(81)90042-6
- Victor Guillemin and Alejandro Uribe, Clustering theorems with twisted spectra, Math. Ann. 273 (1986), no. 3, 479–506. MR 824435, DOI 10.1007/BF01450735
- V. Guillemin and A. Uribe, Monodromy in the quantum spherical pendulum, Comm. Math. Phys. 122 (1989), no. 4, 563–574. MR 1002831
- 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
- Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI 10.1007/BF02392052
- Bertram Kostant, Quantization and unitary representations. I. Prequantization, Lectures in Modern Analysis and Applications, III, Lecture Notes in Mathematics, Vol. 170, Springer, Berlin, 1970, pp. 87–208. MR 0294568
- François Trèves, Introduction to pseudodifferential and Fourier integral operators. Vol. 1, University Series in Mathematics, Plenum Press, New York-London, 1980. Pseudodifferential operators. MR 597144
- Alan Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J. 44 (1977), no. 4, 883–892. MR 482878
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- 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