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An uncertainty principle on hyperbolic space


Author: Li Min Sun
Journal: Proc. Amer. Math. Soc. 121 (1994), 471-479
MSC: Primary 43A85; Secondary 22E30, 42C10
DOI: https://doi.org/10.1090/S0002-9939-1994-1186137-8
MathSciNet review: 1186137
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Abstract: In this paper, we establish an uncertainty principle on hyperbolic space $ {H^n} = S{O_e}(n,1)/SO(n)$, which prohibits f from being confined to small neighborhoods around any point in $ {H^n}$ under certain assumptions on the Fourier transform $ \tilde f$, where f is a normalized $ {L^2}$ function on $ {H^n}$.


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  • [1] S. Helgason, Groups and geometric analysis: integral geometry, invariant differential operators, and spherical functions, Pure and Appl. Math., vol. 113, Academic Press, Orlando, 1984. MR 754767 (86c:22017)
  • [2] -, Paley-Wiener theorems and surjectivity of invariant differential operatores on symmetric spaces and Lie groups, Bull. Amer. Math. Soc. 79 (1973), 129-132. MR 0312158 (47:720)
  • [3] R. S. Strichartz, Uncertainty principles in harmonic analysis, J. Funct. Anal. 84 (1989), 97-114. MR 999490 (91a:42017)
  • [4] -, Harmonic analysis as spectral theory of Laplacians, J. Funct. Anal. 87 (1989), 51-148. MR 1025883 (91c:43015)
  • [5] R. Takahashi, Sur les représentations unitaires des groupe de Lorentz généralisés, Bull. Soc. Math. France 91 (1963), 289-433. MR 0179296 (31:3544)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1186137-8
Keywords: Hyperbolic space, uncertainty principle
Article copyright: © Copyright 1994 American Mathematical Society

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