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On $ L\sb{p}$-spectra of the laplacian on a Lie group with polynomial growth

Author: A. Hulanicki
Journal: Proc. Amer. Math. Soc. 44 (1974), 482-484
MSC: Primary 22E30
MathSciNet review: 0360931
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Abstract: The following theorem is proved: If $ G$ is a Lie group with polynomial growth (a compact extension of a nilpotent group, e.g.) and $ \Delta = X_1^2 + \cdots + X_n^2$, where $ {X_1}, \cdots ,{X_n}$ is a basis of the Lie algebra of $ G$, then for all $ p,1 \leqq p < \infty $, the operator $ \Delta $ has the same spectrum on all $ {L_p}(G)$.

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Article copyright: © Copyright 1974 American Mathematical Society