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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:328

Article

Hasanov, M.

关键词: resolvent;    operator functions;    eigenvectors;    eigenvalues;   

DOI  :  10.1016/j.jmaa.2006.06.017

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free