On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics

Mark S. Ashbaugh; Lotfi Hermi

doi:10.1216/RMJ-2008-38-4-1037

On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics

Mark S. Ashbaugh
, Lotfi Hermi

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Using spherical harmonics, rearrangement techniques, the Sobolev inequality, and Chiti's reverse Hölder inequality, we obtain extensions of a classical result of Payne, Polya, and Weinberger bounding the gap between consecutive eigenvalues of the Dirichlet Laplacian in terms of moments of the preceding ones. The extensions yield domain-dependent inequalities.

Original language	English (US)
Pages (from-to)	1037-1072
Number of pages	36
Journal	Rocky Mountain Journal of Mathematics
Volume	38
Issue number	4
DOIs	https://doi.org/10.1216/RMJ-2008-38-4-1037
State	Published - 2008

Keywords

Dirichlet eigenvalue problem for domains in euclidean space
Domain-dependent inequalities for eigen-values
Eigenvalues ot the laplacian
H.C. Yang inequality
Hile-protter inequality
Payne-pólya-weinberger inequality

ASJC Scopus subject areas

General Mathematics

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10.1216/RMJ-2008-38-4-1037

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abstract = "Using spherical harmonics, rearrangement techniques, the Sobolev inequality, and Chiti's reverse H{\"o}lder inequality, we obtain extensions of a classical result of Payne, Polya, and Weinberger bounding the gap between consecutive eigenvalues of the Dirichlet Laplacian in terms of moments of the preceding ones. The extensions yield domain-dependent inequalities.",

keywords = "Dirichlet eigenvalue problem for domains in euclidean space, Domain-dependent inequalities for eigen-values, Eigenvalues ot the laplacian, H.C. Yang inequality, Hile-protter inequality, Payne-p{\'o}lya-weinberger inequality",

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doi = "10.1216/RMJ-2008-38-4-1037",

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pages = "1037--1072",

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T1 - On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics

AU - Ashbaugh, Mark S.

AU - Hermi, Lotfi

PY - 2008

Y1 - 2008

N2 - Using spherical harmonics, rearrangement techniques, the Sobolev inequality, and Chiti's reverse Hölder inequality, we obtain extensions of a classical result of Payne, Polya, and Weinberger bounding the gap between consecutive eigenvalues of the Dirichlet Laplacian in terms of moments of the preceding ones. The extensions yield domain-dependent inequalities.

AB - Using spherical harmonics, rearrangement techniques, the Sobolev inequality, and Chiti's reverse Hölder inequality, we obtain extensions of a classical result of Payne, Polya, and Weinberger bounding the gap between consecutive eigenvalues of the Dirichlet Laplacian in terms of moments of the preceding ones. The extensions yield domain-dependent inequalities.

KW - Dirichlet eigenvalue problem for domains in euclidean space

KW - Domain-dependent inequalities for eigen-values

KW - Eigenvalues ot the laplacian

KW - H.C. Yang inequality

KW - Hile-protter inequality

KW - Payne-pólya-weinberger inequality

UR - https://www.scopus.com/pages/publications/50249089527

UR - https://www.scopus.com/pages/publications/50249089527#tab=citedBy

U2 - 10.1216/RMJ-2008-38-4-1037

DO - 10.1216/RMJ-2008-38-4-1037

M3 - Article

AN - SCOPUS:50249089527

SN - 0035-7596

VL - 38

SP - 1037

EP - 1072

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 4

ER -

On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics

Abstract

Keywords

ASJC Scopus subject areas

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