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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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New range theorems for the dual Radon transform
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by Alexander Katsevich PDF
Trans. Amer. Math. Soc. 353 (2001), 1089-1102 Request permission

Abstract:

Three new range theorems are established for the dual Radon transform $R^*$: on $C^\infty$ functions that do not decay fast at infinity (and admit an asymptotic expansion), on $\mathcal {S}(Z_n)$, and on $C_0^\infty (Z_n)$. Here $Z_n:=S^{n-1}\times \mathbb {R}$, and $R^*$ acts on even functions $\mu (\alpha ,p)=\mu (-\alpha ,-p), (\alpha ,p)\in Z_n$.
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Additional Information
  • Alexander Katsevich
  • Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
  • MR Author ID: 320907
  • Email: akatsevi@pegasus.cc.ucf.edu
  • Received by editor(s): January 20, 1998
  • Received by editor(s) in revised form: June 24, 1999
  • Published electronically: October 11, 2000
  • Additional Notes: This research was supported in part by NSF grant DMS-9704285
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 1089-1102
  • MSC (2000): Primary 44A12
  • DOI: https://doi.org/10.1090/S0002-9947-00-02641-6
  • MathSciNet review: 1804413