2010/10/11 by Jean-Philippe Anker, Anker, Jean-Philippe, Vittoria Pierfelice +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · doi:10.48550/arxiv.1010.2137
openalex publication_date 2010/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the Laplace-Beltrami operator Δon Damek-Ricci spaces and derive pointwise estimates for the kernel of exp(τΔ), when τ∈ C* with Re(τ) ≥ 0. When τ∈ iR*, we obtain in particular pointwise estimates of the Schrödinger kernel associated with Δ. We then prove Strichartz estimates for the Schrödinger equation, for a family of admissible pairs which is larger than in the Euclidean case. This extends the results obtained by Anker and Pierfelice on real hyperbolic spaces. As a further application, we study the dispersive properties of the Schrödinger equation associated with a distinguished Laplacian on Damek-Ricci spaces, showing that in this case the standard dispersive estimate fails while suitable weighted Strichartz estimates hold.