Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows

Juan Antonio Barcelo; Luca Fanelli; Susana Gutierrez; Alberto Ruiz; Mari Cruz Vilela

doi:10.1016/j.jfa.2013.02.017

Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows

Juan Antonio Barcelo, Luca Fanelli, Susana Gutierrez, Alberto Ruiz, Mari Cruz Vilela

Mathematics

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11 Citations (Scopus)

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Abstract

We prove a logarithmic convexity result for exponentially weighted L-norms of solutions to electromagnetic Schrödinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega. © 2013 Elsevier Inc.

Original language	English
Pages (from-to)	2386-2415
Number of pages	30
Journal	Journal of Functional Analysis
Volume	264
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2013.02.017
Publication status	Published - 15 May 2013

Keywords

math.AP
35J10, 35L05

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10.1016/j.jfa.2013.02.017

Gutierrez_Hardy_uncertainty_principle_Functional_Analysis_2013
NOTICE: this is the author’s version of a work that was accepted for publication in the above journal. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, [VOL 264, ISSUE 10, 2013. DOI: 10.1016/j.jfa.2013.02.017
Accepted author manuscript, 395 KBLicence: None: All rights reserved

Cite this

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AU - Antonio Barcelo, Juan

AU - Fanelli, Luca

AU - Gutierrez, Susana

AU - Ruiz, Alberto

AU - Cruz Vilela, Mari

PY - 2013/5/15

Y1 - 2013/5/15

N2 - We prove a logarithmic convexity result for exponentially weighted L-norms of solutions to electromagnetic Schrödinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega. © 2013 Elsevier Inc.

AB - We prove a logarithmic convexity result for exponentially weighted L-norms of solutions to electromagnetic Schrödinger equation, without needing to assume smallness of the magnetic potential. As a consequence, we can prove a unique continuation result in the style of the Hardy uncertainty principle, which generalizes the analogous theorems which have been recently proved by Escauriaza, Kenig, Ponce and Vega. © 2013 Elsevier Inc.

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Hardy uncertainty principle and unique continuation properties of covariant Schrödinger flows

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