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A support theorem for a Gaussian Radon transform in infinite dimensions


Authors: Jeremy J. Becnel and Ambar N. Sengupta
Journal: Trans. Amer. Math. Soc. 364 (2012), 1281-1291
MSC (2010): Primary 44A12; Secondary 28C20, 60H40
DOI: https://doi.org/10.1090/S0002-9947-2011-05365-1
Published electronically: November 7, 2011
MathSciNet review: 2869177
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Abstract: We prove that in infinite dimensions, if a bounded, suitably continuous, function has zero Gaussian integral over all hyperplanes outside a closed bounded convex set, then the function is zero outside this set. This is an infinite-dimensional form of the well-known Helgason support theorem for Radon transforms in finite dimensions.


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Additional Information

Jeremy J. Becnel
Affiliation: Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, Texas 75962-3040
Email: becneljj@sfasu.edu

Ambar N. Sengupta
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: sengupta@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2011-05365-1
Received by editor(s): November 4, 2009
Received by editor(s) in revised form: March 17, 2010, and April 6, 2010
Published electronically: November 7, 2011
Additional Notes: The research of the first author was supported by National Security Agency Young Investigators Grant MPO-BA331.
The research of the second author was supported by US National Science Foundation Grant DMS-0601141
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.