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

Hasanov, M.

doi:10.1016/j.jmaa.2006.06.017

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

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Hasanov M.

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

Publication Type: Article / Article
Volume: 328 Issue: 2
Publication Date: 2007
Doi Number: 10.1016/j.jmaa.2006.06.017
Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.1487-1494
Istanbul Technical University Affiliated: No

Abstract

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.