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Growth Estimates for Solutions to the Wave Equation on Damek--Ricci Spaces
Let $\mathcal{L}$ be the positive definite left-invariant distinguished Laplacian, and let $\mathrm{d}ρ$ denote the right Haar measure on a Damek--Ricci space $S$. Let $u(t,x)$ denote the solution to the wave equation $\partial_t^2 u + \mathcal{L} u=0$ with initial data $(u,\partial_t u)|_{t=0}=(f,g
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