A class of nonlinear equations in Hilbert space and its application to completeness problems

Hasanov M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.328, no.2, pp.1487-1494, 2007 (SCI-Expanded) identifier identifier


Nonlinear equations arising in the spectral theory of self-adjoint operator functions and related completeness problems for eigenvectors are studied. A separation theorem about the values of the Rayleigh functional on solutions of a nonlinear equation is proved. This theorem is used, as a new approach to establish completeness of eigenvectors for some classes of self-adjoint operator functions. Examples from matrix pencils are given. (c) 2006 Elsevier Inc. All rights reserved.