Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones

2020/10/24 by Zhang, Junyong · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.12838

Abstract

We construct the Schwartz kernel of resolvent and spectral measure for Schrödinger operators on the flat Euclidean cone (X,g), where X=C(\mathbbS_σ¹)=(0,∞)× \mathbbS_σ¹ is a product cone over the circle, \mathbbS_σ¹=\R/2πσ\Z, with radius σ>0 and the metric g=dr²+r² dθ². As products, we prove the dispersive estimates for the Schrödinger and half-wave propagators in this setting.

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