A CLASS OF NONLINEAR EIGENVALUE PROBLEMS.

Abstract

The report considers the nonlinear eigenvalue problem (A - B(lambda))x = 0 in a Hilbert space, where A = or > 0 is compact and B(lambda) is a polynomial with nonnegative operator coefficients, satisfying B(0) = 0. It is shown that if A and B(lambda) are in certain operator classes, then there exists an unconditional basis of the Hilbert space consisting of eigenvectors x corresponding to nonnegative eigenvalues lambda. It is also shown that the nonnegative eigenvalues can be characterized by variational principles. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1967
Accession Number
AD0662738

Entities

People

  • R. E. L. Turner

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Eigenvalues
  • Eigenvectors
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Polynomials
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Linear Algebra

Technology Areas

  • Space