Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Heisenberg uniqueness pairs in the plane. Three parallel lines


Author: Daniel Blasi Babot
Journal: Proc. Amer. Math. Soc. 141 (2013), 3899-3904
MSC (2010): Primary 42B10; Secondary 31B35, 81Q05
Published electronically: July 18, 2013
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A Heisenberg uniqueness pair is a pair $ (\Gamma ,\Lambda ),$ where $ \Gamma $ is a curve in the plane and $ \Lambda $ is a set in the plane, with the following property: any bounded Borel measure $ \mu $ in the plane supported on $ \Gamma ,$ which is absolutely continuous with respect to arc length and whose Fourier transform $ \widehat {\mu }$ vanishes on $ \Lambda ,$ must automatically be the zero measure. We characterize the Heisenberg uniqueness pairs for $ \Gamma $ as being three parallel lines $ \Gamma =\mathbb{R}\times \{\alpha ,\beta ,\gamma \}$ with $ \alpha <\beta <\gamma ,$ $ (\gamma -\alpha )/(\beta -\alpha )\in \mathbb{N}.$


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B10, 31B35, 81Q05

Retrieve articles in all journals with MSC (2010): 42B10, 31B35, 81Q05


Additional Information

Daniel Blasi Babot
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Cerdanyola del Vallès, Catalunya, Spain
Email: dblasi@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11678-3
PII: S 0002-9939(2013)11678-3
Keywords: Heisenberg uniqueness pairs, uncertainty principle
Received by editor(s): March 29, 2011
Received by editor(s) in revised form: October 29, 2011, and January 23, 2012
Published electronically: July 18, 2013
Additional Notes: The author was partially supported by the Göran Gustaffson Foundation, grant No. 2009SGR00420, and the DGICYT grant MTM2008-00145
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.