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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Characterization of eigenfunctions of the Laplacian by boundedness conditions


Author: Robert S. Strichartz
Journal: Trans. Amer. Math. Soc. 338 (1993), 971-979
MSC: Primary 42B10; Secondary 35J05, 35P05, 43A80
MathSciNet review: 1108614
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Abstract: If $ {\{ {f_k}(x)\} _{k \in \mathbb{Z}}}$ is a doubly infinite sequence of functions on $ {\mathbb{R}^n}$ which are uniformly bounded and such that $ \Delta {f_k} = {f_{k + 1}}$, then $ \Delta {f_0} = - {f_0}$. This generalizes a theorem of Roe $ (n = 1)$. The analogous statement is true on the Heisenberg group, but false in hyperbolic space.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1108614-1
PII: S 0002-9947(1993)1108614-1
Article copyright: © Copyright 1993 American Mathematical Society