Characterization of eigenfunctions of the Laplacian by boundedness conditions
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- by Robert S. Strichartz PDF
- Trans. Amer. Math. Soc. 338 (1993), 971-979 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 338 (1993), 971-979
- MSC: Primary 42B10; Secondary 35J05, 35P05, 43A80
- DOI: https://doi.org/10.1090/S0002-9947-1993-1108614-1
- MathSciNet review: 1108614