Affine Weyl Groups and the Boundary Value Eigenvalue Problems of the Laplacian

Yoshinori HOSHIKAWA; Hajime URAKAWA

doi:10.4036/iis.2010.93

Interdisciplinary Information Sciences

Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050

Regular Papers

Affine Weyl Groups and the Boundary Value Eigenvalue Problems of the Laplacian

Yoshinori HOSHIKAWA, Hajime URAKAWA

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Keywords: affine Weyl group, Dirichlet eigenvalue problem, Neumann eigenvalue problem, eigenvalue, eigenfunction

JOURNAL FREE ACCESS

2010 Volume 16 Issue 1 Pages 93-109

DOI https://doi.org/10.4036/iis.2010.93

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Abstract

In this paper, we give the explicit formulas for the eigenvalues, and the eigenfunctions, of the Dirichlet and also the Neumann eigenvalue problems of the Laplacian on the crystallographic Euclidean domains. We show the Poisson summation formulas of the Dirichlet and Neumann heat kernels.

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