Spectral projection operators of the Sub-Laplacian and Laguerre calculus
on non-degenerate nilpotent Lie groups of step two
Spectral projection operators of the Sub-Laplacian and Laguerre calculus
on non-degenerate nilpotent Lie groups of step two
In this paper, we introduce the spectral projection operators $\mathbb{P}_m$ on non-degenerate nilpotent Lie groups $\mathcal{N}$ of step two, associated to the joint spectrum of sub-Laplacian and derivatives in step two. We construct their kernels $P_m(\mathbf{y},\mathbf{t})$ by using Laguerre calculus and find a simple integral representation formula for $\mathbf{y}\neq 0$. …