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Currently displaying 1 – 3 of 3

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Spherical distributions on harmonic extensions of pseudo- $H$ -type groups.

Ciatti, Paolo — 1997

Journal of Lie Theory

A Clifford algebra approach to simple Lie algebras of real rank two. I: The $A_{2}$ case.

Ciatti, Paolo — 2000

Journal of Lie Theory

Transferring $L^{p}$ eigenfunction bounds from $S^{2 n + 1}$ to hⁿ

Valentina Casarino; Paolo Ciatti — 2009

Studia Mathematica

By using the notion of contraction of Lie groups, we transfer $L^{p} - L ²$ estimates for joint spectral projectors from the unit complex sphere $S^{2 n + 1}$ in $ℂ^{n + 1}$ to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.

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