Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones

Junyong Zhang

doi:10.1016/j.jfa.2021.109311

Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones

Junyong Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We construct the Schwartz kernel of resolvent and spectral measure for Schrödinger operators on the flat Euclidean cone (X,g), where X=C(S_σ¹)=(0,∞)×S_σ¹ is a product cone over the circle, S_σ¹=R/2πσZ, with radius σ>0 and the metric g=dr²+r²dθ². As products, we prove the dispersive estimates for the Schrödinger and half-wave propagators in this setting.

Original language	English
Article number	109311
Journal	Journal of Functional Analysis
Volume	282
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2021.109311
Publication status	Published - 1 Feb 2022

Keywords

Dispersive estimates
Flat cone
Resolvent kernel
Spectral measure

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10.1016/j.jfa.2021.109311

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title = "Resolvent and spectral measure for Schr{\"o}dinger operators on flat Euclidean cones",

abstract = "We construct the Schwartz kernel of resolvent and spectral measure for Schr{\"o}dinger operators on the flat Euclidean cone (X,g), where X=C(Sσ1)=(0,∞)×Sσ1 is a product cone over the circle, Sσ1=R/2πσZ, with radius σ>0 and the metric g=dr2+r2dθ2. As products, we prove the dispersive estimates for the Schr{\"o}dinger and half-wave propagators in this setting.",

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AB - We construct the Schwartz kernel of resolvent and spectral measure for Schrödinger operators on the flat Euclidean cone (X,g), where X=C(Sσ1)=(0,∞)×Sσ1 is a product cone over the circle, Sσ1=R/2πσZ, with radius σ>0 and the metric g=dr2+r2dθ2. As products, we prove the dispersive estimates for the Schrödinger and half-wave propagators in this setting.

KW - Dispersive estimates

KW - Flat cone

KW - Resolvent kernel

KW - Spectral measure

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DO - 10.1016/j.jfa.2021.109311

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VL - 282

JO - Journal of Functional Analysis

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ER -

Resolvent and spectral measure for Schrödinger operators on flat Euclidean cones

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Keywords

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