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


Hasanov M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.328, sa.2, ss.1487-1494, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 328 Konu: 2
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1016/j.jmaa.2006.06.017
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.1487-1494

Özet

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.