Spectrum of the nonself-adjoint Schr�dinger operator in unbounded regions

Abstract

REGIONS UDC 513 9It is proved that the discrete spectrum of the operator -~ + q(x) in the space L2(E2k) (k -> ~)t where q(x) is a measurable complex-valued function satisfying the condition ~(x) l ---Ce -~ |xl, having no finite limit points, and for k =1 the discrete spectrum consists of a finite number of points.Consider the minimal operator A n generated by the differential operator

On the number of eigenvalues of the discrete one-dimensional Schrödinger operator with a complex potential

“…Most of the papers listed below contain results on the eigenvalues of non-selfadjoint operators. More specifically, those are the articles [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][19][20][21][22][23][24][25]28,29]. The remaining references were needed for technical reasons.…”