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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bounds for ratios of eigenvalues of the Dirichlet Laplacian
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by Mark S. Ashbaugh and Rafael D. Benguria PDF
Proc. Amer. Math. Soc. 121 (1994), 145-150 Request permission

Abstract:

We use a doubling scheme to derive a bound for the ratio of the ${2^k}$th eigenvalue to the first for the Dirichlet Laplacian on a bounded domain $\Omega \subset {\mathbb {R}^n}$. The explicit bounds we obtain derive from the optimal bound ${({\lambda _2}/{\lambda _1})_\Omega } \leq {({\lambda _2}/{\lambda _1})_{n -{\text {dimensional ball}}}}$ (the Payne-Pólya-Weinberger conjecture) recently proved by us.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 145-150
  • MSC: Primary 35P15; Secondary 35J05
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1186125-1
  • MathSciNet review: 1186125