A Singular Critical Potential For The Schrödinger operator

We construct a potential $V$ on $\RR^d$, smooth away from one pole, and a sequence of quasi-modes for the operator $-\Delta+V$, which concentrate on this pole. No smoothing effect, Strichartz estimates nor dispersive inequalities hold for the corresponding Schrödinger equation.

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Source https://hal.science/hal-00000760
Author Duyckaerts, Thomas
Maintainer CCSD
Last Updated June 2, 2026, 07:35 (UTC)
Created June 2, 2026, 07:35 (UTC)
Identifier hal-00000760
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Laboratoire de Mathématiques d'Orsay (LMO) ; Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
creator Duyckaerts, Thomas
date 2003-10-20T00:00:00
harvest_object_id fa4378e8-881c-4959-aafa-834833350e73
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2024-10-23T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/math.AP/0310309
set_spec type:UNDEFINED