On $L_{p}$-spectra of the laplacian on a Lie group with polynomial growth
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- by A. Hulanicki PDF
- Proc. Amer. Math. Soc. 44 (1974), 482-484 Request permission
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 ${L_p}(G)$.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 482-484
- MSC: Primary 22E30
- DOI: https://doi.org/10.1090/S0002-9939-1974-0360931-2
- MathSciNet review: 0360931