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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Eigenfunctions of the Laplacian
on rotationally symmetric manifolds


Author: Michel Marias
Journal: Trans. Amer. Math. Soc. 350 (1998), 4367-4375
MSC (1991): Primary 58G25, 60J45
DOI: https://doi.org/10.1090/S0002-9947-98-02354-X
MathSciNet review: 1616007
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Abstract: Eigenfunctions of the Laplacian on a negatively curved, rotationally symmetric manifold $M=(\mathbf{R}^n,ds^2),$ $ds^2=dr^2+f(r)^2d\theta ^2,$ are constructed explicitly under the assumption that an integral of $f(r)$ converges. This integral is the same one which gives the existence of nonconstant harmonic functions on $M.$


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Additional Information

Michel Marias
Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54.006, Greece
Email: marias@ccf.auth.gr

DOI: https://doi.org/10.1090/S0002-9947-98-02354-X
Keywords: Rotationally symmetric manifolds, radial curvature, eigenfunctions, harmonic functions, heat kernels, diffusion processes, subordination measure.
Received by editor(s): July 16, 1995
Received by editor(s) in revised form: January 18, 1996
Article copyright: © Copyright 1998 American Mathematical Society