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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 328 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1016/j.jmaa.2006.06.017
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.1487-1494

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.