Spectral properties of a certain class of complex potentials. (English) Zbl 0525.58036


58J50 Spectral problems; spectral geometry; scattering theory on manifolds
53C30 Differential geometry of homogeneous manifolds
31C12 Potential theory on Riemannian manifolds and other spaces
22E46 Semisimple Lie groups and their representations
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
58C40 Spectral theory; eigenvalue problems on manifolds
35P05 General topics in linear spectral theory for PDEs
Full Text: DOI


[1] M. Berger, P. Gauduchon and E. Mazet, Le spectre d’une variété Riemanniene, Lecture Notes in Math., Vol. 194, Berlin and New York, 1971.
[2] H. D. Fegan, Special function potentials for the Laplacian, Canad. J. Math. 34 (1982), no. 5, 1183 – 1194. · Zbl 0505.47037
[3] Victor Guillemin, Band asymptotics in two dimensions, Adv. in Math. 42 (1981), no. 3, 248 – 282. · Zbl 0478.58029
[4] I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonselfadjoint operators, Translated from the Russian by A. Feinstein. Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. · Zbl 0181.13503
[5] Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. · Zbl 0121.27504
[6] 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.
[7] H. P. McKean and P. van Moerbeke, The spectrum of Hill’s equation, Invent. Math. 30 (1975), no. 3, 217 – 274. · Zbl 0319.34024
[8] P. Sarnak, Spectral behavior of quasiperiodic potentials, Comm. Math. Phys. 84 (1982), no. 3, 377 – 401. · Zbl 0506.35074
[9] 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. · Zbl 0159.15504
[10] A. Uribe, The averaging method and spectral invariants, Ph.D. Thesis, M.I.T., 1982.
[11] Alan Weinstein, Asymptotics of eigenvalue clusters for the Laplacian plus a potential, Duke Math. J. 44 (1977), no. 4, 883 – 892. · Zbl 0385.58013
[12] H. Weyl, The theory of groups and quantum mechanics, Dover, New York, 1950. · Zbl 0041.25401
[13] E. T. Whittaker and G. N. Watson, A course in modern analysis, Cambridge Univ. Press, Cambridge, 1935. · JFM 45.0433.02
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.