Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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

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.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 58G25, 35P99
  • Retrieve articles in all journals with MSC: 58G25, 35P99
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