Shifted wave equation on noncompact symmetric spaces

2025/04/30 by Kuznetsova, Yulia, Song, Zhipeng
#22E30 #35L05 #42B15 #43A85 #43A90 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.21479

Abstract

Let G be a semisimple, connected, and noncompact Lie group with a finite center. We consider the Laplace-Beltrami operator Δ on the homogeneous space G/K=S by a maximal compact subgroup K. We obtain pointwise estimates for the kernel of an oscillating function exp( it√(|x|)) ψ(x) applied to the shifted Laplacian Δ+|ρ|², a case not available before. We obtain a polynomial decay in time of the kernel, and of the L^p'-L^p norms of the operator, for 2

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