A Unified Approach to Universal Inequalities for Eigenvalues of Elliptic Operators

@inproceedings{Ashbaugh2004AUA,
  title={A Unified Approach to Universal Inequalities for Eigenvalues of Elliptic Operators},
  author={Mark S. Ashbaugh and L. Hermi},
  year={2004}
}
  • Mark S. Ashbaugh, L. Hermi
  • Published 2004
An abstract approach to universal inequalities for the discrete spectrum of a self-adjoint operator is presented. The approach is based on commutator algebra, the Rayleigh-Ritz principle, and one set of “auxiliary” operators. The new proof unifies classical inequalities due to Payne-Pólya-Weinberger, Hile Protter, and H. C. Yang and provides a Yang-type strengthening of Hook’s bounds for various elliptic operators with Dirichlet boundary conditions. The proof avoids the introduction of the… CONTINUE READING
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