Pointwise dispersive estimates for Schr "odinger operators on product\n cones

2020/10/19 by Blake Keeler, Keeler, Blake, Jeremy L. Marzuola +1 · 2 citations
Mathematics · #58J50 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2010.09778

openalex publication_date 2020/10/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We investigate the dispersive properties of solutions to the Schr "odinger\nequation with a weakly decaying radial potential on cones. If the potential has\nsufficient polynomial decay at infinity, then we show that the Schr "odinger\nflow on each eigenspace of the link manifold satisfies a weighted L¹\→\nL^\∞ dispersive estimate. In odd dimensions, the decay rate we compute is\nconsistent with that of the Schr "odinger equation in a Euclidean space of the\nsame dimension, but the spatial weights reflect the more complicated regularity\nissues in frequency that we face in the form of the spectral measure. In even\ndimensions, we prove a similar estimate, but with a loss of t^1/2 compared\nto the sharp Euclidean estimate.\n

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