A support theorem for a Gaussian Radon transform in infinite dimensions
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- by Jeremy J. Becnel and Ambar N. Sengupta
- Trans. Amer. Math. Soc. 364 (2012), 1281-1291
- DOI: https://doi.org/10.1090/S0002-9947-2011-05365-1
- Published electronically: November 7, 2011
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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.References
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Bibliographic 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
- 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 - © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2869177