Perturbations of the Spectrum of the Schroedinger Operator with a Complex Periodic Potential
The present article is devoted to an investigation of the discrete spectrum of the nonselfadjoint Schroedinger operator with a complex periodic potential perturbed by a decreasing potential. It is well known  that the spectrum of the unperturbed operator is a purely continuous spectrum situated on a denumerable sequence of arcs in the λ plane.
KeywordsUnit Circle Continuous Spectrum Accumulation Point Edge Point Unit Period
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- 1.F.S. Rofe-Beketov, “The spectra of nonself-adjoint differential operators with periodic coefficients,” Dokl. Akad. Nauk SSSR, Vol. 152, No. 6 (1963).Google Scholar
- 2.B. S. Pavlov, “The nonself-adjoint Schroedinger operator,” in Topics in Mathematical Physics, Vol. 1, Consultants Bureau, New York,(1967).Google Scholar
- 3.J.D. Tamarkin, “On Fredholm’s integral equations whose kernels are analytic in a parameter,” Am. Math., Vol. 28, No. 2 (1927).Google Scholar
- 4.V. A. Zheludev, “Eigenvalues of the perturbed Schroedinger operator with a periodic potential,” in Topics in Mathematical Physics, Vol. 2, Consultants Bureau, New York (1968).Google Scholar
- 5.F. S. Rofe-Beketov, “The criterion for the finiteness of the number of discrete levels introduced into lacunas of the continuous spectrum by a perturbation of a periodic potential,” Dokl. Akad. Nauk SSSR, Vol. 156, No. 3 (1964).Google Scholar
- 6.E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Vol. 2, Oxford University Press (1962).Google Scholar
- 7.V. A. Tkachenko, “The spectral analysis of the one-dimensional Schroedinger operator with a periodic potential,” Dokl. Akad. Nauk SSSR, Vol. 155, No. 2 (1964).Google Scholar