A Unified Approach to Universal Inequalities for Eigenvalues of Elliptic Operators

  title={A Unified Approach to Universal Inequalities for Eigenvalues of Elliptic Operators},
  author={Mark S. Ashbaugh and L. Hermi},
  • 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
Highly Cited
This paper has 20 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
15 Citations
22 References
Similar Papers


Publications referenced by this paper.
Showing 1-10 of 22 references

Estimates of the difference between consecutive eigenvalues

  • H. C. Yang
  • preprint, 1995
  • 1991
Highly Influential
9 Excerpts

Sur le quotient de deux fréquences propres consécutives

  • L. E. Payne, G. Pólya, H. F. Weinberger
  • Comptes Rendus Acad. Sci. Paris, 241
  • 1955
Highly Influential
7 Excerpts

Bounds for ratios of the first

  • M. S. Ashbaugh, R. D. Benguria
  • second, and third membrane eigenvalues, in…
  • 1996
Highly Influential
5 Excerpts

Inequalities for eigenvalues of the Laplacian

  • G. N. Hile, M. H. Protter
  • Indiana Univ. Math. J., 29
  • 1980
Highly Influential
6 Excerpts

The universal eigenvalue bounds of Payne–Pólya–Weinberger

  • M. S. Ashbaugh
  • Hile– Protter, and H.C. Yang, Proc. Indian Acad…
  • 2004
Highly Influential
6 Excerpts

Domain-independent upper bounds for eigenvalues of elliptic operators

  • S. M. Hook
  • Trans. Amer. Math. Soc., 318
  • 1990
Highly Influential
5 Excerpts

General bounds for the eigenvalues of Schrödinger operators

  • II E.M. Harrell
  • ‘Maximum Principles and Eigenvalue Problems in…
  • 1988
Highly Influential
5 Excerpts

Commutator bounds for eigenvalues of some differential operators

  • E. M. Harrell, P. L. Michel
  • ‘Evolution Equations’
  • 1300
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…