Spectral properties of a certain class of complex potentials
HTML articles powered by AMS MathViewer
- by V. Guillemin and A. Uribe
- Trans. Amer. Math. Soc. 279 (1983), 759-771
- DOI: https://doi.org/10.1090/S0002-9947-1983-0709582-8
- PDF | Request permission
Abstract:
In this paper we discuss spectral properties of the Schroedinger operator $- \Delta + q$ on compact homogeneous spaces for certain complex valued potentials $q$. We show, for instance, that for these potentials the spectrum of $- \Delta + q$ is identical with the spectrum of $- \Delta$.References
- M. Berger, P. Gauduchon and E. Mazet, Le spectre d’une variété Riemanniene, Lecture Notes in Math., Vol. 194, Berlin and New York, 1971.
- H. D. Fegan, Special function potentials for the Laplacian, Canadian J. Math. 34 (1982), no. 5, 1183–1194. MR 675684, DOI 10.4153/CJM-1982-081-3
- 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
- I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by A. Feinstein. MR 0246142
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- H. P. McKean, Integrable systems and algebraic curves, Global analysis (Proc. Biennial Sem. Canad. Math. Congr., Univ. Calgary, Calgary, Alta., 1978) Lecture Notes in Math., vol. 755, Springer, Berlin, 1979, pp. 83–200. MR 564904
- H. P. McKean and P. van Moerbeke, The spectrum of Hill’s equation, Invent. Math. 30 (1975), no. 3, 217–274. MR 397076, DOI 10.1007/BF01425567
- P. Sarnak, Spectral behavior of quasiperiodic potentials, Comm. Math. Phys. 84 (1982), no. 3, 377–401. MR 667408
- R. T. Seeley, Complex powers of an elliptic operator, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 288–307. MR 0237943 A. Uribe, The averaging method and spectral invariants, Ph.D. Thesis, M.I.T., 1982.
- Alan Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J. 44 (1977), no. 4, 883–892. MR 482878 H. Weyl, The theory of groups and quantum mechanics, Dover, New York, 1950. E. T. Whittaker and G. N. Watson, A course in modern analysis, Cambridge Univ. Press, Cambridge, 1935.
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 279 (1983), 759-771
- MSC: Primary 58G25; Secondary 35P99
- DOI: https://doi.org/10.1090/S0002-9947-1983-0709582-8
- MathSciNet review: 709582