Spectral properties of a Schrodinger equation with a class of complex potentials and a general boundary condition

[摘要] In this paper we investigate the spectrum and the spectral singularities of an operator L generalized in L-2(R+) by the differential expression l(y) = y(n) - Sigma(k=0)(n-1)lambda(k)q(k)(x)y, x epsilon R+ = [0, infinity), and the boundary condition integral(0)(infinity) K (x) f (x) dx + alphaf' (0) - betaf (0) = 0 where lambda is a complex parameter, q(k), k = 0, 1, . . . , n - 1, are complex valued functions, q(0), q(1), . . . , q(n-1) are differentiable on (0, infinity), K epsilon L-2(R+), and alpha, epsilon C with \alpha\ + \beta\ not equal 0. Discussing the spectrum we obtain that L has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions lim(x-->infinity) q(k)(x) = 0, sup(x epsilon R+) {e(epsilonrootx){Sigma(k=0)(n-1)\q'(k)(x)\ + \K(x)\}} < infinity hold, where k = 0, 1, . . . , n - 1 and epsilon > 0. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-10-01

[关键词] Sturm-Liouville operator;spectrum;spectral singularities;non-selfadjoint differential operator