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Transactions of the American Mathematical Society

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Sharp Hardy uncertainty principle and gaussian profiles of covariant Schrödinger evolutions


Authors: B. Cassano and L. Fanelli
Journal: Trans. Amer. Math. Soc. 367 (2015), 2213-2233
MSC (2010): Primary 35J10, 35L05
DOI: https://doi.org/10.1090/S0002-9947-2014-06383-6
Published electronically: September 22, 2014
MathSciNet review: 3286512
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Abstract: We prove a sharp version of the Hardy uncertainty principle for Schrödinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of Schrödinger evolutions. We provide, in addition, an example of a real electromagnetic potential which produces the existence of solutions with critical gaussian decay, at two distinct times.


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Additional Information

B. Cassano
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro 5, 00185-Roma, Italy
Email: cassano@mat.uniroma1.it

L. Fanelli
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, P.le A. Moro 5, 00185-Roma, Italy
Email: fanelli@mat.uniroma1.it

DOI: https://doi.org/10.1090/S0002-9947-2014-06383-6
Keywords: Schr\"odinger equation, electromagnetic potentials, unique continuation, uncertainty principle
Received by editor(s): October 1, 2013
Published electronically: September 22, 2014
Additional Notes: The authors were supported by the Italian project FIRB 2012 Dispersive Dynamics: Fourier Analysis and Calculus of Variations.
Article copyright: © Copyright 2014 American Mathematical Society