On the spectral theory of nonselfadpoint Schrödinger operators
by
B.P. Allahverdiev
Department of Mathematics, Suleyman Demirel University

Denote by ((-*, *);E)(dimE=n < *) the Hilbert space of vector functions consider the differential expression Schroedinger , -**x**, where -continuos matrix- valued function on (-*, *).Let us denote by the closure of the minimal operator [10] generated by (1), and by its domain. Let the matrix-valued function Q(x) be such that the symmetric operator has deficiency index (2n, 2n). Thus, we first describe all the maximal dissipative extensions of the symmetric operator in terms of the boundary conditions. For example we construct a selfadjoint dilation of a dissipative operator, carry out a spectral analysis of a dilation, use the Lax-Phillips scattering theory, and find the schattering matrix of a dilation. We determine the characteristic function of a dissipative operator and investigate its analytic properties. Finally, we prove a theorem on the completeness of the eigenfunctions of a dissipative operator.

Date received: February 12, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-37.