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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Dynamical versions of Hardy’s uncertainty principle: A survey
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by Aingeru Fernández-Bertolin and Eugenia Malinnikova HTML | PDF
Bull. Amer. Math. Soc. 58 (2021), 357-375 Request permission

Abstract:

The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. The textbook proof of the result, as well as one of the original proofs by Hardy, refers to the Phragmén–Lindelöf theorem. In this note we first describe the connection of the Hardy uncertainty to the Schrödinger equation, and give a new proof of Hardy’s result which is based on this connection and the Liouville theorem. The proof is related to the second proof of Hardy, which has been undeservedly forgotten. Then we survey the recent results on dynamical versions of Hardy’s theorem.
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Additional Information
  • Aingeru Fernández-Bertolin
  • Affiliation: Universidad del País Vasco /Euskal Herriko Unibertsitatea (UPV/EHU), Dpto. de Matemáticas, Apartado 644, 48080 Bilbao, Spain
  • ORCID: 0000-0002-5772-7249
  • Email: aingeru.fernandez@ehu.eus
  • Eugenia Malinnikova
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California; and Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
  • MR Author ID: 630914
  • ORCID: 0000-0002-6126-1592
  • Email: eugeniam@stanford.edu
  • Received by editor(s): August 13, 2020
  • Published electronically: June 3, 2021
  • Additional Notes: The first author was partially supported by ERCEA Advanced Grant 2014 669689 - HADE, by the project PGC2018-094528-B-I00 (AEI/FEDER, UE) and acronym “IHAIP”, and by the Basque Government through the project IT1247-19.
    The second author was partially supported by NSF grant DMS-1956294 and by the Research Council of Norway, project 275113.
  • © Copyright 2021 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 58 (2021), 357-375
  • MSC (2020): Primary 42A38, 35B05
  • DOI: https://doi.org/10.1090/bull/1729
  • MathSciNet review: 4273105